I asked you earlier to attempt to define this gender ideology of which you speak. What in precise terms is 'trans ideology'?
I've offered this before. It's the notion that people have a nebulous unquantifiable thing called a gender identity which may differ from their biological sex. It's akin to the notion of a soul as far as I can see.
Gender critical people such as myself see it as "woo". Obviously there is nothing wrong with believing in gender identity any more than there is in believing in God, a soul or homeopathy - until it actively causes problems and hurts people. Thus in the same way that we strongly advise people that if they are ill, science is the best bet rather than magic water or sky people, we should be careful that if someone says "I'm a woman because my gender identity is female even though I have a male body" that we don't crack out the hormone pills and prep the operating theatre - not least because these things are irreversible and can go catastrophically wrong.
Similarly if someone says "you must believe in my God and follow my beliefs" the default British position tends to be "piss off". You can believe in your God and if someone is interested in what you say, that's fine, but don't tell everyone else they are wrong. This is analogous to the belief in gender identity whereby people are being told they must announce their pronouns, use non-gendered terms or be cancelled / prevented from holding an event purely for having a different viewpoint or wanting to discuss the issue in a fair way.
There are people who think that it is abhorrent that JKRowling receives huge volumes of rape and death threats for asking in the mildest way that we stop treading on women's rights and women's safety. There are other people who think she should be raped / killed etc because she's a TERF. Personally I find that latter group abhorrent.