(this will be USA-centric)
There is nothing in actual law that says birth certificates define sex for purpose of marriage, at least anywhere in the USA that I've looked into (I'd love to hear I'm wrong with a citation of law). Seriously - government passes laws about "one man, one woman" and then never bothers to define man or woman (or the more correct male and female terms).
There's administrative rules for things like driver's licenses, passports, and social security. But each agency has different rules and their rules don't apply anywhere else. Birth certificates are generally covered by administrative rules.
For marriage itself, I don't know of any administrative rules that define male or female - I only know of case law that does this. Different states have made different decisions. In most places, no decision has been made.
So, what this means is that a marriage between a same sex or opposite gender partners where one partner is trans (pre- or post- op) and the other is not is NOT valid everywhere in the country, no matter what birth certificates, social security cards, passports, driver's licenses, or marriage licenses say. That's the sad truth. The only marriages gauranteed to be valid for trans people are a marriage to another trans person of the same surgical status (post- or pre-) but of opposite gender.
I'm in this situation myself, and it sucks. There's several issues involved:
1) Am I considered married where my wife and I got married? That state's law's matter. If that state decides I'm not married, I'm not, no matter where I am currently. Sometimes this can happen after being issued a marriage license. Also, just because they don't require proof of birth certificate in some jurisdictions doesn't mean that what the birth certificate says doesn't matter. Some jurisdictions have said your genitals matter. Other jurisdictions have said DNA is what matters. So you need to know what the marriage jurisdiction says.
2) The state I live in also matters for things like taxes. If they ban same-sex marriage, and some random court decides on DNA or original birth certificate as the key determination, then I'm not married, at least in that state. That affects things like employment and state taxes and inheritance.
3) The state where I am currently in matters too. If my wife were with me in the wrong county in, say, Texas, we would not be considered married, and I'd lose things like next of kin status if she were injured there.
4) The feds - because of DOMA, the feds don't recognize same sex marriage. But because there is no case law on what makes someone male or female for the purpose of marriage, this could any day be decided any which way.
So, right now, life is a big gray area for us. What it should be is that the birth certificate, DL, etc, documents a physical reality that overrides any errors or incorrect documents (that's usually how documentary evidence is handled in court - it can help prove something, but if the actual thing can be shown to be in disagreement with the documentation, the documentation is ignored).
If you love your potential spouse, and want to marry, I encourage you to - with eyes open and real legal advice (find a lawyer!) - go ahead and get married. That's what I did - if someone decides to tell me I'm not married, they'll have a fight on their hands. Because it's unlikely most of us will ever have a marriage challenged, my marriage is relatively secure - but my family and hers wouldn't sue, nor do we have any insurance dependent upon marital status. But it could be invalidated none-the-less. The IRS could decide I've committed tax fraud for the last 5 years by marking "married" on the form. I could end up in jail for lying to a public official when I got my marriage license. Etc. But I believe that would be unjust and wrong, and I believe love matters way more than those sorts of consequences - I know I'm male, my wife is female, and that makes us opposite sex. And I'm willing to fight if someone challenges that. But I also know what the consequences are if I lose that battle, and I'm willing to deal with it since the other option would be to not marry.
My advice to you if you do get married: marry in a state that requires only a DL to get the license. This won't make it more or less legal, but will cause less questions by the clerk. All your documentation should reflect that you are opposite sex partners. Move from a state or jurisdiction that has decided DNA or original birth certificate is what is important (for instance, parts of Texas) if you live there - no use in being somewhere where you KNOW your marriage is invalid. Rather, move somewhere that either has affirmed your marriage or is ambiguous but hopefully will affirm it soon. Don't mention trans/surgery/etc to the clerk when you get your license (you don't want them to write new regulations if they don't have any to handle it today!). My other advice would be to marry and live in a state that recognizes same-sex marriage, but make sure you still are seen - as much as possible - as opposite sex for marriage to maintain federal recognition. But that option wasn't an option for me, and likely isn't for you.
I do think legal same-sex marriage is the quickest route to fix this problem. If same sex couples can marry, than sex of each partner becomes moot. And same-sex marriage is needed simply to right a historical wrong. But unfortunately the same-sex marriage battle has caused trans marriages to be MORE at risk than they used to be - we're seen as a threat to the status quo, as if a person can change their sex and now can get married to someone they couldn't have married before doing so, that would imply that the natural order isn't quite as fixed as the right wing nuts would like - and it starts to make gender/sex restrictions look kind of stupid. So we're now under attack.
