In general, conservatives claim that sex and gender are the same thing. It’s probably not true of all conservatives, but when most conservative pundits and influencers have made this claim at some point, it’s fair to say that it is the view of the conservative movement. It’s not a strawman, it’s not made up, it’s a claim regularly made by the conservative movement, and if you think “the right” means “all right-wingers” in this scenario, that’s you’re problem because noone else but you thought that.