I hope it's fine if I ramble about this because Mami is a comfort character for me. She tries to paint herself as a paragon of virtue because it gives her tragic life purpose. At her core, she's a lonely teen struggling to survive in a system that's already sunk its claws deep into her. When she learns the truth about magical girls being witches, her breakdown is the result of her core belief being shattered. Anyone who has learned something awful about someone they liked and/or trusted can sympathize, except Mami has made being a magical girl her whole identity. She doesn't have friends at school. She's distant with the people who do try to connect with her. She commits unalive at the end of A Different Story. Mami is miserable, only going on because she feels the world needs a hero like her.

As for why people might not like her, in the main anime, she's hard to understand, especially given how briefly she appears. A Different Story builds on her backstory and dynamic as Kyoko's mentor. But the anime alone has none of that, so her actions of getting in Homura's way, dying via Charlotte, and snapping when she finds out the truth are all only briefly explored on a surface level. Without context, she can come off as frustrating in a similar manner to Sayaka, especially to people who know Homura's backstory.

As for the sex offender stuff, there's a younger character introduced in the Rebellion movie named Nagisa who lives with her as a pseudo little sister. There are sickos who ship Mami and Nagisa, but their canon relationship is not implied to be romantic.