Haha, I am just nitpicking now, but your state used the wrong terms in their
statute:
Quote§ 51-1.2. Marriages between persons of the same gender not valid.
Marriages, whether created by common law, contracted, or performed outside of North Carolina, between individuals of the same gender are not valid in North Carolina.
They should've used "sex" not "gender" if they wanted to keep you and your girlfriend from getting married there.

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When the time comes to get married as male and female in the State we reside in would we need to go back to DC to get annulled? Would the change of my birth certificate just automatically make the marriage we will already have legal in the State we live in? I have no idea and thought maybe someone else might or has been through something similar.
You need very specific reasons and circumstances to get an annulment, such as the marriage was illegal (like you were underage or only doing it to get a green card) or you guys never consummated the marriage, etc. You'd need to use the annulment laws from Washington, D.C. which can be found in Chapter 9, title 16, section 903, which references 46-401.01 and 46-403. (sorry, I'd link it if Panera's internet didn't suck so bad). D.C. law doesn't state that getting married in another state is grounds for an annulment.
So, you can't get an annulment simply because you want to get remarried in another state.
Now, we need to see what NC says, can you get married in NC if you're married in DC (without getting a DC divorce first, since you likely won't qualify for a DC annulment)? It's strangely silent except for a brief mention in 51-8.2 on whether you can be married in another state at the same time, but I am sure we can safely assume that it's a no, but the intention of the law saying you can't be married in another state while marrying in NC is likely for people who want more than one wife or husband, not someone going to marry the same person all over again. In your case, it's basically like signing a contract to buy a specific product in NY and then later on going and resigning the thing in NC. So, would they really say "no you can't get married here" just because you're already married? Would that happen to straight people? Since being married in more than one place
to the same person likely isn't subverting the purpose of the law, just saying this is your "first" marriage on the NC application isn't likely going to make your NC marriage automatically void (in a way, it's still your first marriage even if you do it twice), or if you do say "second" marriage and on the line which asks if the first ended in death, annulment, divorce, etc. you could just write in something like "we're still together and we're remarrying here in NC" and then just go and see what the clerk says.
Now, since that's a big sticky issue there on whether you need a divorce of if you can just marry her again in NC, why don't we just see if you can just
amend the DC marriage license? After you get all your markers changed, could you go back and amend your DC to say "M" and "F" instead of "F" and "F"? (do marriage licenses even state your sex?) Upon it being amended, I don't see why it wouldn't be valid in NC, assuming you'd be legally able to marry in NC if you weren't married in DC.
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Now question for you Simon, is there any reason why you two have decided to get married before your marker changes? Is it mainly for tax purposes (only your federal taxes would be affected if you continue living in NC after your DC marriage)? If you want to marry for other purposes-like, confirming your bond together-could you just have a ceremony to celebrate your commitment and then get legally married once you change your markers?
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And, I am also just adding in for people who don't know me, that I am not an attorney, and even if I was, law is very jurisdictionally based so whatever is said here on Susan's might not be applicable elsewhere. Everyone, including Simon, is encouraged to see a licensed professional in his/her own jurisdiction.