[] People are complicated. Millions of tiny features contribute to their actions, and nobody can account for all of them. But.
[] Sayaka is... Loyal, hardworking when she puts her mind to it, strong moral compass... And highly judgemental, with low self-esteem and lower self-worth. For the most part, these traits define who she is, what she does, and how she sees the world.
-[] Stemming from those, and from her youth and lack of experience, she sees the world in black and white. Either someone is a good person with forgivable flaws, or a bad person who might do something decent on occasion but isn't to be trusted... and she makes conclusions about who falls into which category really, really quickly.
--[] It makes her a great friend, someone who will never believe bad things about you, someone who takes your enemies as her own... Just as long as you're not in conflict with another of her friends who she admires more greatly or is closer to.
---[] She values Madoka the most. Then Mami, who she takes as a role model due to her low self-worth and her morals, seeing Mami as a Hero of Justice where she sees herself as just a talentless poor girl. Hitomi falls in there somewhere, but you're much less clear on that. And then the trouble has always been that Sayaka decides Kyubey is good people and doesn't trust or admire Homura enough to place her over Kyubey.
----[] How that actually happens is complicated, and you don't have much information to work with, but it's some blend of Mami trusting Kyubey and Kyubey making good first impressions. You're almost certain it's mostly that Mami trusts Kyubey -- Mami is who Sayaka wants to be, from Sayaka's point of view, so she can't have bad people as her friends.
-----[] Once Sayaka sees Kyubey as a "good person who might have forgivable flaws," and doesn't view Homura more highly than Kyubey... Then it's "Why would Kyubey do that," and what she really means when she says that is "I am not willing to believe you telling me that Kyubey is actually evil." And more recently, when Homura makes a poor first impression on Sayaka, usually coming off as cold, then Sayaka categorizes her as a bad person for it and promptly will believe things like "Homura is the reason Mami is dead," because that's what bad people do, right?
------[] Here, that's been turned on its head from the moment Mami broke down crying about Kyubey being an evil bastard in front of Sayaka. Sayaka admires Mami a helluva lot more than Kyubey -- Mami is the nice cake-baking senpai who risks her life fighting monsters, in Sayaka's eyes, while Kyubey is just kind of there. And so the moment Mami turns on Kyubey, Sayaka believes, and then Kyubey is evil. Meanwhile, Homura is Mami's friend, and Mami can't have bad people as her friends, so Homura is a good person who might have forgivable flaws. Things kind of stay in limbo for a while, because Sayaka hasn't figured out a way to forgive what she sees as Homura's flaws -- and then Walpurgisnacht is explained, and suddenly Homura is Captain Ahab, all abrasive and sketchy and unfriendly but actually she's at heart a good person out to kill a giant monster. Now Homura is Sayaka's friend and a good person, and... well, Sayaka stands by and helps her friends.
---[] As for her tendency to get herself killed through bullheaded idiocy... It's a product of her lack of self worth, her contact with Mami, her rich and/or to her eyes more talented friends, and her morals, and in many ways these things are exacerbated here. Sayaka feels on some level that she's lived her life in the shadow of others, and even that she pulls them down, that she doesn't have anything to contribute to society. Homura may have heard her sometimes say that she doesn't really know what she wants to do with her life... in being a Magical Girl, Sayaka finds a calling. Problem is it's not in being a Magical Girl, but in being the kind of Magical Girl that Mami is. Selflessly protecting others from witches is, she decides, what she can do where Kyousuke has violin, where Hitomi is rich and talented. Add in a good dose of grief and she's totally willing to throw away her own life... and then she also rejects help from anybody she thinks of as a bad person, because bad people aren't to be trusted and therefore accepting their help isn't to be done.
[] ... Put together, all of this is, by the by, why you believe Sayaka in particular, here, would react positively to Homura's past. Telling her about it doesn't work when she's thinking of Kyubey as a good person, or Homura as a bad person. But things are reversed. She wants to believe good things about Homura because Homura is a good person. She'll readily believe bad things about Kyubey because it's a bad "person."
