Well, in regards to the OP, I did have an Future-Tech spacefairing nation-RP that pretty much was a bio-engineered post-fallout race with similar qualities.
(~6 years ago, reason I still remember it is because the forum still exists and I had to copy-paste some technology developed for that so I could do a quick RP that also occurred in space [they needed a ship that didn't break the laws of physics])
-Made planning long-distance voyages... interesting. Also, redecorating on a mass-budget is easy if you have a welding-torch. Refitting them for a space-suit was always a challenge, though.

As for how I would deal with it, I would ask that person (Do they want me to succeed with someone else? Do they want help? Do they wish to pursue a relationship [fake or real]?) and hope they would respect my own wishes, as their friend.
-Any character would likely try to be equally pragmatic and anti-dramatic. But in my experience, shit just happens.

Also, if it were a biological thing, chances are society has adapted over time to deal with it (not entirely smoothly, but life would continue without pause). But since emergence is a biological thing that occurs to increase the breeding population -because extinction is bad- society would try to strongly assimilate the transgender person ASAP.