This whole "you have to jump through hoops to correct a DMV mistake" is insane to me. Shouldn't you just be able to show a correct, probably unmodified birth certificate to get it corrected!? Oh, red tape.
And nthing the "no one looks at gender marker" line, here. As a cashier, I have never looked at a gender marker on a DL/LP when checking ID for beer, cigs, etc. People base their gendering of you off what you look like, and if they "can't tell", your name.
Grace, I think the gender marker might be just because we're a slightly backwards nation that hasn't moved past that point yet. Best guess.