Many women are wary of entering feminist debates over transgender issues because they are frightened of the reaction, the comedian and writer Jo Brand has said.

Brand was addressing a debate that has led to feminists such as Germaine Greer and Julie Bindel being “no-platformed” at some universities.

She said that reaction was “pathetic” and the two sides needed to see there was common ground. The big danger was that women avoided the debate.

“A lot of people feel very wary about talking about the topic,” Brand said. “A lot of women feel if they say anything at all there is a kind of knee-jerk reaction of anger which has nothing to do with the content of what they said … and because they feel frightened of being threatened. I mean, who wouldn’t be?”

Brand was at the Cheltenham literature festival discussing her new book, Born Lippy, which is in part a “guide to being female”.

She said reading The Female Eunuch changed her life and she lamented the vilification of Greer.

“I understand the feelings that Germaine Greer is trying to express. I understand the reason why trans activists have responded to it in that way, but I kind of feel if both sides just stopped shouting at each other and talked about it they would actually find a way of expressing their feelings without all this kind of hatred for each other.”

She said people on both sides of the debate were being aggressive and they should sit down and talk in a more mature way. “People are picking up opinions that aren’t necessarily being expressed and the whole thing has blown up into a massive great wall of argument that now can’t be torn down.

“I think there’s a lot of infighting with feminism and feminists being quite nasty to each other depending on which camp they’re in. I would rather it was a broad church. We should be able to be adult.”

Brand said some of the things Greer said were “slightly bonkers or off the wall”. But she added: “The fact is Germaine Greer is virtually the mother of modern feminism and it is disrespectful, it is a phasing out of history, to treat her in the way that people do.”

The comedian has two daughters in their late teens and she praised their strength. “Women are much more confident. I look at young women of my daughters’ age – they just won’t take any crap any more in a way we did and I feel very proud of that.”

Brand’s career has ranged from performing under the name the Sea Monster on the comedy circuit in the 1980s to presenting The Great British Bake-Off: An Extra Slice. She said she was never the militant, man-hating feminist of tabloid imagination. But she also rejected the idea that she was moving towards “national treasure” status. She hoped there was still an element of danger about her.

Her appearance presenting Have I Got News for You late last year, at the early stages of the #MeToo movement, was memorable, as she explained the effects of sexism on women to a panel of four men.

Brand said it was not planned. “I don’t really know why I did it like that because I much prefer to say, ‘Shut the fuck up!’ For some reason I didn’t do that. Maybe I thought I’d get the point across better if I didn’t shout in their faces.”