With whom are you arguing? Who is the right? Did the right say anything about gender and sex being a different thing? Why are you assuming that some kind of people thinks differently on that matter?
This has nothing to do with the right. If you want to argue with people, you should do so instead of posting and pretending that someone made a claim. I know it is something a lot of people do online but I think it doesn’t really help making sens of things and it mostly serve the purpose to divide from each other by picturing some kind of boogeyman out of a group of people.
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.