This is kind of how I picture the dymanics between Snape and the Evans family
Art by pojypojy. I can’t find the original online. Click the picture to see full size.
Mr. and Mrs. Evans look different in my head!canon (I have Mrs. Evans looking like a plumper and slightly shorter version of Lily, and I have Mr. Evans sharing Petunia’s coloring and not having a mustache), but this is kind of the general vibe for their behavior and attitude towards Severus, as I imagine it. I also have Mr. and Mrs. Evans believing that Severus and Lily are both sweet on each other (and in my head!canon, Lily was def. sweet on Snape but could never figure out if he was just having hormones or loved her romantically and there’s also the issue of her worrying first and foremost about holding onto the friendship, since Severus was going off the rails with bad friends and actions). My version of Mr. and Mrs. Evans viewed Severus like family (he was over at the Evans house so much it seemed like he lived there) and would have been happy to see Lily and Severus date (although there would be parental concerns about what they might do and Mr. Evans wouldn’t like to think of them doing anything beyond hand holding and light closed-mouth kissing). I figure that since Petunia felt so much like the unfavorite, Mr. and Mrs. Evans had quite different views than Petunia and probably liked Severus and were very open minded in general, much to Petunia’s chagrin. I also figure that Lily may have gotten her tendancy to woobiefy the people she loves a bit from her parents, who may have excused some of Snape’s lack of social graces based upon knowing that he had a difficult homelife.