The regulations pertaining to the National Instant Criminal Background Check System (NICS) at 28 CFR 25.7 require the sex of the transferee in order to conduct a firearms background check. This information is captured on the ATF Form 4473, question #6, which requires the transferee to indicate his/her sex (not gender) by checking or filling in the applicable box adjacent to “Male” or “Female”. Transferees must select either “Male” or “Female”, but cannot choose both or write in “X” regardless of what is recorded on the transferee’s identification document. If the transferee refuses to complete question #6 then the FFL may not transfer the firearm.
If there is a Stairway to Heaven, is there an Escalator to Hell?
If God wanted men to play soccer, he wouldn’t have given us arms. - Mike Ditka
Well, sex is an Immutable (thus far) biological and genetic characteristic. You're either XX or XY (unless you're part of the tiny percentage that's XXY or XYY or some other chromosomal anomaly).
The chromosomes are what they are, and they don't change, no matter what surgery, hormones, etc are administered.
Maybe someday, medical science will be able to take the Y of the guy who's channeling Shania Twain and saying "Man, I feel like a woman" and turn that Y into a second X. But AFAIK, that's way, way way out in Sci-fi land right now.