I can only judge what I see in the game, right now I don't know the episodes on rooster you're talking about, of course I believe you.
It seems obvious to me that Jill doesn't find Tybalt's company annoying, otherwise at least when she's alone with Bella she would sometimes complain about it, instead she laughs when Bella speaks badly about him, which is almost the same attitude she has when Bella speaks badly about MC, it's all Bella's character's fault, not Tybalt's.
when Tybalt interrupts their yoga class, Jill would have every reason in the world to stay with her friends, Jill isn't a Prep, so she listens to Tybalt out of interest, if it was just out of kindness then she shouldn't suddenly leave her best friend, without even saying goodbye.
even worse when Bella proposes Mc to her for a date, why should it be a problem for Jill what could Tybalt think about it? the fact that she doesn't want to annoy him means that a minimum of friendship (to friendzon him...) is there
Then it's normal that if Tybalt directly attacks Mc or Bella, Jill gets in the way, but basically always going along with Tybalt.
when Tybalt wants to get MC kicked out because he wasn't invited, Jill "invents" an excuse to let him stay, she doesn't argue about the merits of kicking him out
Does it seem normal to you that he wants to kick out a person Jill is talking to?
But I don't consider it a serious fault, Jill and Tybalt speak the same language, if he wasn't a jerk he would be a terrible contender for MC.
You are right that in BADIK many characterizations are caricatures, but not only Tybalt's.