Mocking someone’s inconsistent statements, or willful ignorance, or bad behavior towards others, is one sort of thing.
Mocking someone’s physical inabilities, illness, built-in appearance, ethnic heritage, or other unchangeable things about them is something else entirely.
Mocking things that are theoretically changeable, but not really changeable without changing the person’s nature, such as religion; or often not changeable in practice even when theoretically changeable, such as poverty or weight or skill; seems to me to fall in the second class, not the first.
Whether something is “funny” isn’t, I think, the real issue. There are people who genuinely find it funny when somebody’s harmed in one way or another. And it’s possible for the same person to find the same thing simultaneously funny and despicable. Even if something’s funny, that doesn’t automatically make it OK.
And Parker was wrong. Ridicule can very definitely be a weapon. As with nearly any weapon, there are cases in which it’s justifiable to use it, and cases in which it’s wrong to use it.
YMMV. I don’t think Cooper’s funny at all. She is famous for lip syncing to Donald Trump talking… I really don’t get it. Thee’s no original joke there. Her actual standup material is mediocre.
In my opinion, your distinction between the two is somewhat arbitrary. Sometimes it is the case that these character traits of the former category are the product of or incident to something belonging to the latter category. I think religion makes for an excellent case-in-point, because you seem to admit that a person’s choice of religion falls into this latter category, yet it must be acknowledged by all that adherence to at least some major religions necessarily leads to either inconsistency, willful ignorance, or bad behavior.
I very much doubt that the adherents of the religions agree with that. So I don’t see that it’s acknowledged by all.
In any case, mocking specific bad behavior that’s related to a religious belief isn’t the same thing as mocking being a member of the religion. And what I’ve listed in the former category aren’t character traits, they’re specific expressions of behavior.