Voldemort Never Understood
Rab's the perfect pureblood heir, impeccably trained, cultured and educated to assume his role as head of an ancient line. Yet Rabastan had never been interested in using his position to gain power or influence over others.
Rabastan had the position Tom Marvolo Riddle should have had.
Rabastan was very much loved by his parents. Always had anything he needed, and was pretty much given everything he ever wanted, even though he never asked for much except opportunities to explore.
Voldemort was abandoned by his father and deserted by his mother (I think he'd see her death as desertion). He grew up never having anything of his own and having to steal to get anything he wanted. Rabastan had everything Tom Riddle ever wanted.
Rabastan loves the diversity of the human race and sees value in muggle and magical alike. Because he's embraced all types of people, he's been accepted and embraced in return (at least before he became a Death Eater).
Voldemort felt that muggles were worthless and purebloods were too weak to take their proper place (again my take on his psychology). Voldemort had been denied the advantages of his birthright by both parents and held down by the rules of society. He would believe Rabastan was 'soft' and 'weak' for not taking advantage of his station.
Rabastan's self-worth is tied up in learning all he can and using his abilities to benefit the world around him. He feels completely at home in almost any situation because he is as willing to follow as he is to lead. And when Rabastan leads, he leads as teacher would, with the intent to train others how to care for themselves rather than making them indebted to him for his help.
Tom Riddle needed to control everyone and everything to prove his own self-worth. Voldemort seeks to be awe inspiring and have people owe him. Voldemort did not lead others, he controled them.
People who take the time to get to know Rabastan Lestrange as a person, and not just a name, trust him, and with good reason. Rabastan can absolutely be counted on to deliver on his word. He does not let his own personal issues (of which he has many) get in the way of doing what he believes is the right thing. Rabastan has his own personal code of ethics, one that started in the training he received from his father in the responsibilities of the Lestrange Family, but developed into something profoundly spiritual as he grew and explored other cultures. Rabastan is holy in a way he doesn't really perceive as being as unusual as it is. His view of life as being sacred and respecting that there are things unknowable that just need to be taken on faith, is consistent with the view of many spiritual leaders throughout history.
Voldemort reveres nothing but himself. He viewed Rabastan's black and white morality as childish and his faith as ridiculous and the Lestrange ethics as just talk.
Because of the purity of Rabastan's intent to do no harm, his acceptance of other cultures, and his willingness to learn, Rabastan has been taught many religious and spiritual secrets of groups he's lived among, he's also been smart enough to bind himself to those secrets so that he cannot be coerced into divulging them.
People didn't trust Tom Riddle, they confided in him because of the tricks he used, not the person he was. Voldemort would be jealous of Rabastan's ability to get people to confide their secrets in him.
No, I don't doubt at all that Voldemort hated Rabastan, but he'd want him on his side.