[jimmygrapes]

I have no references for this but my guess would be related to the idea that there are two genders and those genders cannot/should not be changed. Most of the time when I see people ask your question they are trying to draw out something to do with racism, but that's really quite the strawman; very few conservatives are seeking the ability to use racial slurs under the guise of free speech.

[yurtolo]

I think what people are getting banned from social media for is scepticism of the concept of 'gender identity', particularly when it is used to override the material reality of sex.

It's not only a viewpoint held by many conservatives, but also basically all radical feminists, who are the polar opposite to conservatives in both general political stance and their reasoning behind rejecting the ideology of gender identity. From my observations, in practice it seems to be the radical feminists getting censored for this on social media much more than the conservatives.