peter is a #manhater in this au and he's much more willing to be around women. he will be actively hostile towards batman, nightwing, red hood, and robin but with spoiler, huntress, black bat, and oracle? he's a polite young man and wouldn't dream of disrespecting them. not out of a sense of like... "oh women are weaker than men so i can't hit them" it's literally just cause he's reacting to his trauma and his anger and distrusts men so much. it's a big reason why tim and peter do NOT get along for a while, but peter and selina get along pretty well. (selina pov of peter is like "aww he's feral and keeps trying to bite us" like someone finding a stray kitten). peter is always angry and always bitter and he's not a saint by any means. but he is far more willing to be around and work with women. (it's the trauma). however, he's still distrusting of them
which means that when steph shows up, tim is APPALLED when peter stands near her, banters with her, and even laughs at her jokes. he is pouty and huffy the entire time. but steph mistakes peter's banter as trust and tim is very smug when peter blatantly shows her that he doesn't trust her at all and that they aren't friends