I have this problem with my 21 year old daughter. She at a college for music and drama, so very creative, emotional types and she is completely indoctrinated. We had a bit of a debate about it in the car one day but she gets very defensive and teary. What gets me is she's really sporty and has played football for over a decade, so I kept coming back to the effect trans ideology will have on women's sport. It won't be long now and there will be 3 fully intact biological males on the winners podium at women's events!
I was a dancer, so in that art world.
I'm also very liberal in general. But I had to get there on my own.
Just keep having polite discussions, because when it gets heated it further entrenches those opinions. My mum was anti trans, not very, but against children, and I thought she was awful for it, now her opinion is right.
Is your daughter a reader? One of the things that really changed my mind was the book Invisible Women by Caroline Criado Perez. It made me realise how fundamentally stupid it was to same that men are the same as women just because they've decided to me. It also made me realise that it was men again pushing this agenda and silencing us all, yet again.