In BC we can't change that until after a hysto. I didn't use to mind but the stupid new care cards now actually have it printed on the card and that sucks. My driving license says M and my care card says F! Urgh! Most visits they don't look but when they see it it either gets a weird look or they point out it's wrong. It's stupid. The only people who need to know are those treating, not the receptionists! But hey, eventually I'll get that hysto and rid of the wrong marker.
But yeah, not worth trying to change it without it being legally acceptable, especially in Wall Street run US healthcare! If you need any major, expensive treatment, they get a team of folks to find a way not to fund it. If they discovered then that you deceived them by changing your gendermarker without it being legally valid where you are, that's fraud and say goodbye to the treatment you really need! And yes, they WILL figure that out, and fast. That's a denying team's dream right there!