I’m not saying you have to like it, but I see a lot of people saying it is out of character to have Tigerstar fall in love with a kittypet because of his anti-half-clan views. This is nonsense of course, as if you look carefully, Tigerstar is actually one of the less prejudice cats in the series.
When he first meets Firepaw he’s actually quite interested in seeing how he’ll do in the clan. Up till this point the only things he knows about him is that he’s a kittypet and that he defeated Longtail. When he’s training with the other apprentices, Tigerclaw praises Firepaw for being able to learn something while his own apprentice hasn’t. It really isn’t until Tigerclaw discovers that Firepaw knows about his plans does he start to hate him.
Later, he uses rogues and kittypets to attack the clan camp. In Tigerclaw’s Fury, it is shown quite clearly that he admires strength and doesn’t really care where it comes from. He hates other based on how much advantage he would have in hating them. In TigerClan, he knew it would help the clan unite if he made half clans the common enemy and so targeted them. But he really has nothing against them personally.
It is the same case with Sasha. When he meets her, she is already a rogue, trying to survive on her own with no experience. He teaches her and finds she’s a quick learner. Add in the natural attraction factor and it’s not hard to see why they would be mates.
Tigerstar is only upset at Pinestar for choosing the kittypet lifestyle over a warrior one. He does pretty much the same to Sasha when she refuses to join ShadowClan, calling her “nothing”. For him, it is not where you are born, but what you choose to accept.