Critics have accused the Harry Potter author of being transphobic, an allegation she strongly denies.
In June 2020, she wrote an essay explaining how she was partly motivated to speak about transgender issues because of her experience of domestic abuse and sexual assault.
Appearing on Piers Morgan’s show on TalkTV, Cox compared cancel culture to a form of fascism.
The 75-year-old Scottish actor, who plays media magnate Logan Roy in the hit HBO drama, said: “It is a kind of modern day McCarthyism really. It is a kind of raid on people’s sensibilities in order to reduce them and make them… I don’t know, there is so much hypocrisy in the whole thing.
“I find the whole thing completely hypocritical. I am not religious but there is a thing in the bible where it says, ‘Let he or she without sin cast the first stone’ and there seems to be a lot of casting of stones. And it is like a virus.”
Morgan referenced comments by billionaire Elon Musk, who has described what he calls a “woke virus” in modern society.
Cox responded: “It is total fascism. You are absolutely right. It is total fascism…You see, it is hypocrisy again. The hypocritical notion of ‘I am being liberal’ but actually you are being fascist and people should just stop it and behave themselves.”
Harry Potter film stars Emma Watson, Daniel Radcliffe and Eddie Redmayne are among those who have publicly disagreed with Rowling over her comments about gender.
Cox said he had previously not felt comfortable addressing the issue of JK Rowling but added: “I thought there was something deeply unjust about it. And I just felt that.
“It is happening time and time again. It is not only the people who are cancelled. It is also people like their families, like their children, like their parents.
“It has such ramifications. It creates like an earthquake situation.”
Cox also appeared to defend Hollywood actor Bill Murray after Searchlight Pictures suspended production on the film Being Mortal to investigate a complaint filed against him.
Murray, 71, has since described the incident as “a difference of opinion”.
Cox said: “In my business it catches because suddenly projects (are affected). Bill Murray the other day, he made a remark and was taken in a way of being offensive. The picture he was making was stopped, the whole thing.
“Bill went on, I think it was CNN, and explained himself, I thought rather brilliantly, saying, ‘It’s about times that have changed, I grew up in one time and I am meeting another time and it is very hard to know how to approach that time’.
“Where do we go? How do we come in? Where is the entry way to make a conversation, to make even a joke with one another.”