Canon
Kuchiki Byakuya:***** Renji's captain, and the man who commands his utmost respect and allegiance in Kannagara. Apart from their professional relationship as captain and lieutenant shinigami, however, their interactions might be described as similar to that of siblings. Simply because Byakuya is his captain does not mean Renji will refrain from prodding at him or snickering when Kakashi always manages to get under his skin. He thinks Byakuya is too uptight and will often make jokes at his expense or try to drag him out to social gatherings like the picnic. He might think his superior can be an ass but he does genuinely respect and like the man, even if he thinks Byakuya needs to lighten up.
He can act immature and childish around the other man too, whining/sulking/pouting/all of the above if Byakuya tells him to do something he doesn't want to but has no legitimate objection beyond laziness/pettiness (though he isn't shy about defying an order if he does genuinely disagree with it).
Byakuya is also one of the only people capable of reigning in Renji's temper, smothering it with his cold, no-bullshit demeanor and generally being able to ease it into something more productive.
Because of their vastly different backgrounds, Renji and Byakuya see the world in completely different ways. Far from Byakuya's world where appearances and reputation are everything, Renji firmly believes actions speak louder than words and appearances are fickle. He puts very little stock in other peoples' opinions of him unless they have the power to back it up--he still very much has his eleventh division history and Rukongai background in him at that. Life in Rukongai was so hard, at odds with Byakuya's privileged childhood, so he doesn't take a lot for granted and tries to enjoy himself whenever he can--the idea of work before fun is still something he has to adjust to around Byakuya. He also is much more open with his emotions than Byakuya, and tries to bring that out in his captain as well.
Hisana Kuchiki: *** Byakuya's dearly departed wife and the woman who abandoned Rukia in Rukongai so long ago. Renji has mixed feelings towards this woman, feeling that his friendship with Rukia is in part due to what she did, but also understanding Rukia's resentment over having been abandoned. Part of him is a little miffed he had to give up his room to her and sleep in the kitchen. She is Byakuya's wife though, and so he does always treat her with due respect.
Kuchiki Rukia:***** [Dropped] His best friend from childhood, Rukia, while she was in Kannagara, was the single most important person to Renji. His loyalty to her, both in canon and in Kannagara is absolutely unquestionable, her safety and well-being of highest priority to Renji. He's in love with her, and doubts he will ever fall for anyone else, which is discouraging as he knows the impossibility of the idea.
He was at first a little upset by the distance Rukia seemed to show when they arrived, which was only exacerbated by the Hitomi's showing of dreams, showing the both of them the hidden misgivings and regrets of the other. Relations between Byakuya and Rukia didn't help theirs either, as his ties to Byakuya made her pull away from the both of them, retreating to Raisato to live with Rin. He got angry at Byakuya for not telling Rukia to stay in Hisato, and when Rukia died, he was absolutely crushed and wanted to go out on a monster-killing rampage until Byakuya calmed him down.
He was beyond relieved when Rukia was revived and things were on the up and up between them as Byakuya and Rukia began to patch up their issues as well. Their relationship as best friends was almost back to normal again when Erotic Dream Week struck. Rukia had a nightmare about being gangraped and killed in Rukongai, which shook Renji to his core because of how possible it was for them, back then, and worries about what his life would have turned out like if she had died before they became shinigami. Then came his own dream, and Rukia learned about the feelings he had for her, which he'd never told her about and which it became clear she didn't seem to share. But before the repercussions of this could be dealt with, Rukia disappeared. It was a rough blow for Renji, and he initially went to the picnic partially just to get his mind off of it.
Kannagara
Allen Walker: * Renji met this guy when he stepped in to defend a girl he was calling out for being naive. They had an...interesting argument in which they both basically agreed but Renji's coarseness continued to offend Allen while Renji considered Allen's attitude condescending and superior, leading to them talking in circles around each other and arguing syntax. They did manage to eventually come to a civil conclusion and haven't spoken much since. Renji was amused at Allen's surprise that he was familiar with Rukia and Ukitake, both more polite and formal than him.
Asano Rin: *** Renji met this girl on the first day he arrived in Kannagara. She was the one who first told him that Rukia was in Kannagara, and after initially trading names, Renji didn't really pay much attention to her for a while. Soon though, it became evident that she was close to Rukia, and after Rin took care of Rukia after her revival from death, Renji thanked her for doing so, and she asks him if she is interested in joining the search expedition for the gods. They have a few more lighthearted meetings after this, once in Hisato and then later at the picnic.
Castiel: * [Dropped] This is probably the strangest guy Renji has ever spoken to. The first time they met was at the picnic, where Castiel was downing jugs of strong alcohol like it was water and they spoke for a short while. The next time was on the network, where Castiel's claiming to "attract cocks" raised some eyebrows. Most recently was a conversation wherein they flipped each other off and finally introduced themselves. He's not really sure what to think of Castiel, but as odd as his manner of speaking is, and his tendency to take everything literally, Renji has taken a liking to the man.
Dokuro Chrome: **** Renji was one of the first to explain Kannagara to Chrome when she arrived, and they've continued speaking, on and off, ever since. There's something about Chrome that appeals to a protective instinct in Renji. It's possibly because she reminds him a great deal of Hinamori Momo, who was a friend at the Academy and went on to become a fellow lieutenant. He also feels a certain kinship with her, in that her devotion to Mukuro mirrors his own to Rukia. They've both seen very deeply personal dreams of each other, and Chrome is one of the people he's closest to in Kannagara. There's little he wouldn't do for her if she asked, and he would do his best to help her (and Mukuro, even, grudgingly) if a situation where she needed it came up.
Fran: * An annoying guy that showed up to tease him when the unicorns and rabbits where running around. Later he found out through a nightmare that there was more to this guy than it seemed, but Fran's lack of agency and will to change a situation that left him afraid of being left behind annoyed him further.
Hatake Kakashi: ** This man has won major points with Renji for the single fact that he can consistently get under Byakuya's skin. The first Renji saw of him was the Valentine's Day video, and overall hasn't spoken to him much, but he usually is helpful and provides good information for the fellow residents of Kannagara, and from the time they fought together during Nightmare Week, he knows Kakashi can be a good ally. He disappeared some time ago, and Renji is not yet aware of his return, as he was dead at the time.
Jessica Hamby: ** A bount vampire. They had an awkward conversation on the matter soon after she arrived and then she saw his dream about Rukia. They recently had another very awkward conversation...on PMS. Still, she's not unpleasant to talk to overall, and he certainly admires her spunk.
Marco: * He's only really talked to this guy a few times and doesn't know much about him. Their only real significant conversation was when Colbert made a post about Aizen and Renji made an ill-fated attempt to warn him away from the man. Marco got the benefit of the warning, and Renji found out a bit about the Yeerk threat in his homeworld. Despite not having spoken with him much, he knows at the least Marco will be a good ally when the shit hits the fan.
Matt:*** Renji doesn't know Matt well, but he likes the guy. He gave Matt the rundown when he first arrived in Kannagara, and the pair of them learned a bit about each other through one of Renji's dreams. He considers Matt a friend and wouldn't mind getting to know him better.
Meguro Gau: *** Renji likes this kid. Gau reminds him a bit of Hanatarou, what with his clumsiness and politeness and timidity. He finds Gau's innocence kind of adorable and he can't help but laugh whenever the kid tries to curse and ends up blushing. It also makes him feel a bit protective over the kid. He'd like to help toughen him up a bit sometime.
Mello: ** [Dropped/Reapped by separate player] Renji and Mello first met for a spar on the day of Sousuke Aizen's arrival, which had left Renji in a thoroughly unpleasant mood to say the least. Then they were united in mutual trolling by a certain Stephen Colbert, who continually insisted that Mello was a "biker chick" and berated Renji first for fighting "her", and then for "hounding a woman (Mello) when she was clearly disinterested." The both of them were pretty much agreed on a desire to pound Colbert into the ground. They had an interesting conversation over one of Mello's dreams and he looked for Renji when he went missing. After that, he disappeared, and returned in the middle of Nightmare Week with no memory of Kannagara. Renji hasn't spoken to him much yet, as he was killed in Nightmare Week and only just revived.
Rokudo Mukuro:* Jackass. Renji would punch this guy in the face if he wasn't important to Chrome. He knows from experience that there superficially unpleasant people can have redeeming qualities when you get to know them and there is probably more to Mukuro than his unpleasant personality, but really, he'd just rather avoid him.
Shimizu Raikou: ** The first time Renji spoke to this man, the gods had turned most of Kannagara's residents into children. Raikou was talking about training, and young!Renji naturally assumed he was a shinigami in-training at the Academy, but found out he wasn't. They then got into an argument about which is better--shinigami or samurai. They spoke once again, as adults--a discussion on fighting, death, honor and duty. It seems that while they differ on some big ideas, they have quite a few in common as well. Raikou's also promised Renji a spar, to "settle" that little argument of theirs on whether shinigami or samurai are better.
Son Goku:* A nice kid. Renji had a spar with him and Mello once. He helped Byakuya look for him when he apparently went missing for three days.
Umino Iruka: ** [Dropped] Kakashi's friend. He's a nice guy, friendly. Iruka took care of himself and Rukia while they were children (which Renji appreciated) and set up the picnic (with taiyaki and sake--free food and alcohol are a surefire way to win points with him!). Renji likes the man, but doesn't have much of an attachment to him. Like Kakashi, he thinks Iruka could be a good ally if something like Nightmare Week happened again.
Yamamoto Takeshi:* "Taichou was so worried that he fell over from worry." He hasn't seen much of this guy since he told him about his captain having been looking for him. Was amused by the guy. Also won points for being able to get under Byakuya's skin like Kakashi.
Key:
* = Neutrality. Renji can't really be bothered to care one way or the other.
** = Renji likes you. He'd probably like to share a drink or a spar, or have lunch with you sometime, but don't expect any deep-seated loyalty or motivation to do anything for you unless he's lacking in other things to do.
*** = Friend status. In some way or another, you've gotten on Renji's good side. He either enjoys talking to you, or respects your abilities in battle. He may occasionally do you small favors or buy you a drink. Also will generally support you unless you're looking to start up some kind of big conflict, in which case he'll leave the decision to his captain.
**** = At this point, you are definitely very important to Renji. He will start going out of his way to protect you, and will be liable to form a dislike of someone purely by proxy of them disliking, insulting, or generally having a problem with you.
***** = If you have reached this level, Renji is extremely close to you and will defend you to his last breath. At the pinnacle of importance to him, either in terms of respect or personal fondness, Renji will not hesitate to lay his life on the line for you. Anything happening to someone of this level will be highly distressing to Renji, and expect to see an emergence of that fiery temper.
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* = Mild dislike/annoyance. Something about you rubs Renji the wrong way. He'll probably snark and cuss at you more than usual.
** = Dislike. Renji either has a personal grievance against you or a dislike-by-proxy. Same as * but stronger. Might go out of his way to be an ass to you.
*** = Strong dislike. This is where Renji might actually start avoiding you to avoid getting in trouble for a brawl. He really can't stand you and would love to punch you in the face...or worse places.
**** = If you've gotten to this level (and this is actually pretty hard), Renji doesn't even care about getting in trouble. If he sees you in person, a brawl will probably happen. He may or may not instigate it himself.
***** = Hatred. Pure, blinding hatred. Renji wants to see you dead, man. If you give cause for Byakuya to allow it, he will try to kill you. You probably have to be a dick of Aizen-level proportions to get this out of Renji.