I agree, it's getting silly and tit for tat by too many people from differing 'sides' - play ground politics.
Agree or disagree, with what people say - criticise them for poor taste. By all means ridicule them, personally ignore them, or choose not to take in their material, but....... blanket cancelling and no platforming them, is the route of deliberately mendacious extremists or the pathetic. You won't persuade me that either entity isn't to blame for the state of affairs we find ourselves in.
Such measures should be reserved for those who invoke or incite harassment, harm or in other words cross the line from free speech to criminality. And when I say criminality, I don't mean judging by the standards of an individual's personal political views; or just because they don't like what somebody else has to say or want to prevent other people hearing their pov.
Carr is a case in point. If he has to stoop to such humour for a pay check that reflects on him. I've never had any intention of watching him and won't be doing so now. However it's comedy and as low/offensive as he went he wasn't inciting anybody to do anything; so if other people want to engage with that they should be allowed to do so as he should be allowed to make his living.
When you want people banned for bad taste jokes at one end, or have liberals/feminists like JK Rowling demonised for having the temerity to make the point of saying we already have a word for people who menstruate at the other end, we really are heading down a hole.
Carr and Rowling have their money in the bank and they will doubtless ride out any storm in comfort, but it's no laughing matter for people who are further down the food chain - it can be life changing and usually disproportionate to what they have said. A good example of that is Bobby Madley.