Right now, at least in WA, I can change my drivers license without having to change anything else. Hoping that changes the police computers, too, if I ever get stopped. However, that's only 1 legal thing that would state the "new"? gender. However, everything else is still the old one. Passport, birth cert, etc. Passport isn't much of an issue unless you travel internationally, but is it good enough for most government related issues that you may face on a daily basis? (Hopefully getting pulled over isn't a daily occurrence).
Each government agency generally gets to decide what they need to convince them that you are M or F.
So DMV might pick one standard but the marriage department another.
And then there are court decisions.
There is no universal definition of sex/gender in law in the USA.
It basically sucks in that regard. That said, I would think *most* agencies would accept what is on your DL.