its an interesting question especially with regard to gender critical feminism because the ideology with regards to trans rights and trans people does match the views of traditionally conservative groups
OP I'm not sure I understand what you think or mean here?
My first take was that you were asserting that ideology around trans rights is Conservative? If so I agree to an extent:
The desire to mask homosexuality by encouraging trans identification seems socially conservative, especially when you consider the forced sex reassignment surgery performed on gay men in Iran.
The fragmentation of people into individuals (over 100 genders, multiple very specific sexualities) is an echo of Thatcher's "There is no such thing as society, only the individual" and is in direct opposition to the class analysis upon which socialism was built.
This fragmentation is also famously employed to encourage us to spend more money (hence the invention of pink for girls, blue for boys). This pro capitalist stance is politically Conservative. Also supported by the way in which trans people are forced to become life long medical consumers - the hormones, the breasts removed or fake breasts added. All makes quite a lot of money for some people!
Reading the rest of your post I'm less clear of your meaning. Perhaps you are not from the UK? Brexit was not split along left /right lines. It was far more about middle class metropolitan elite /the somewhat ignored rest of the population (or racists /anti racists, depending on who you listen to!)
You can't really call being gender critical an ideology. It is just a belief in material reality and science. Whilst I'm a far left aligned socialist and aspiring radical feminist, I still expect many right wingers to understand science and reality, at least in the UK.