Not really in this case because the label given to these people is socially constructed. It's not 'reality' that they are or are not their proclaimed gender, just as it's not reality that they are or are not pretty. Saying that there is some objective reality of their prettiness or ugliness doesn't make much sense either way, in the same way.

It's my opinion that the words man and woman should refer to the biological sex, not the person's desired sex/gender, so I use the words in that way. Obviously some people feel strongly about using the words in the opposite way. That's okay, but I'm just not going to use them that way. Neither of us have a stronger claim to "observable reality", but I think I at least have a stronger claim to historical/traditional normalcy.