Kate kept her cool and some of her arguments may have validity (e.g. venue having the right to formulate their rules as they deem fit) but it seems she cannot or does not want to see the importance of context and seems to be prone to conflation.
In direct context we are dealing with real life people and it makes sense to be careful about what we say to the next person, whereas a comedy show is a stage, a performance with an accepted distance. So her talking about, and comparing, free speech in coffee shops with free speech in a comedy performance doesn’t really compare meaningfully.
As far as I can see: when we go to see a comedian in a show we do not meet a personal, private, direct person. The comedian puts on his/her comedian cloak and may in that role have a bit of a license, perhaps even a duty, to offend.
The audience expects (up to very recently, anyway) and appreciates all things comedy: overstatement, understatement, caricaturing, exaggeration, comparing incomparables, pushing boundaries etc. He/she has a role. She/he is the jester, the rattler, the cheek, the verbal dare-devil, the safety valve on the pressure cooker of society, offering welcome catharses to his/her audience in a humourous, civil enough, safe enough space.
What I found interesting: while Kate is apparently quite happy with censored, sanitised comedy, she does not seem to mind making rather personal, sniding, condescending remarks:
E.g. when she tells Lionel to use a dictionary to find out what the word “racist” means, suggesting he cannot read a dictionary or when she congratulates him on his long career, adding she’s never heard of him.
He, on the other hand, is as far as I can tell just exasperated and disheartened. He expresses himself in a mix of incredulity and dispair.
Not much of what he says is either heard or respected and even willfully distorted. And while he is pretty pissed off he does not set out to personally attack Kate, but rather tries to reach out to her as a mate of the trade, begging her to see what she is signing up for and that by so doing risking to be an accomplice in killing good and meaningful comedy.
It seems to me he sees further down the road, too. Some censorship may or may not be reasonable but where does it end? And who decides? And who needs protection from whom? Again this conflation: her example with children’s shows. Obviously children have to be protected (that goes without saying) but, as he says, over 18 year olds, too?