If you hold gender critical beliefs, do you accept that some people firmly believe they are born in the 'wrong' body,
Sure. Not only do I accept other people's rights to their firm beliefs, I support their right to hold beliefs that I don't share or even that I vehemently disagree with.
and have a right to live as the other sex (up to but not including the point where it would impinge on the rights of that other sex),
I think this is possibly the crux of what "gender critical" means - it means that we are critical of gender itself. If you understand patriarchy to be "a system of social structures and practices in which men dominate, oppress and exploit women" then men being powerful, breadwinning, rulers of the world, made out of little boys who were clever, brave lego-builders while women are supporting, nurturing, keepers of the home, made out of little girls who were dainty pink dolly-cuddlers is integral to that structure. That is what gender is. I cannot subscribe to a system which says that "living as a girl / woman" is equated to femininity under patriarchy.
I think everyone should have the right to dress as they like, enjoy the hobbies they prefer, adopt a name they love, live in romantic relationships with any other consenting adult regardless of sex, and that in an ideal world there would be no such thing as "living as a man / woman" because the whole concept would be redundant.
possibly taking hormones and undergoing surgery? Is this a coherent position to hold?
If a capacitous adult wants to take hormones and undergo surgery I wouldn't want the state to stop them. Any more than the state should stop people getting face tattoos and surgery to give them a forked tongue.