Public speech and insults are a free-for-all. Despite the best efforts of language policing, it’s still a free-for-all.
But there are tiers of insult strength. The insults at the very top - so high up that the air is too thin to breathe, like Everest - are the racial insults. These are, to mix metaphors, the thermonuclear warheads. You really don’t fuck around with them. I’d be surprised if even a black person could get away with calling another black person the N word with that evil rhotic ‘R’ at the end. You just don’t touch them. If you’re white, you really don’t touch them.
The next tier are the religious-based insults. These can be thrown around a little more freely, depending on the audience and the comedian. Religion is kinda-sorta something you choose to belong to, rather than an inborn characteristic like your “race” (the whole concept of race is bullshit, but nevertheless it IS a thing in our society.) They’re still pretty taboo.
A slightly lower tier, I think, are physical and mental disabilities. I think it’s sufficiently understood by society that physical disabilities aren’t something to be mocked, but the taboo just isn’t strong enough to prevent it from happening regularly in comedy.
The lowest tier are the insults that essentially just mean “a shitty person.” Jerk, jackass, asshole…ok, now we’re getting into the territory where parts of the body are the descriptor that’s used to signify “a shitty person.” These parts of the body are, basically, the junk.
Dick, prick, cock, asshole, pussy, schmuck (Yiddish for penis), putz (Yiddish for penis), 'Gatz (Italian for penis), Fangool (Italian for “fuck in the ass”), and what have you. “Cunt” falls into this category.
However, there’s a caveat that women have historically been put down more, specifically because of their junk, than men have. So it’s a bit more of a sore subject.
For whatever reason, “Cunt” is far more gender neutral, and thus far more commonly thrown around, in British comedy (otherwise known as comedy.) Not to slag off/take the piss out of/have a go at the Merchants too much (a rhyming-slang double: merchant = merchant banker = wanker, plus merchant = merchant bank = Yank.) But…compared to the Brits, our comedy is right shit.