Identity is a funny thing. We can all have our inner identities based on whatever matters to us, but this is different from demanding that others also accept them fully. The latter usually requires that third parties verify our identities in some material sense (like a pilot's license for those who identify as bomber pilots).
For instance, I could want (theoretically) to identify as a citizen of some country I find fascinating (France) when I don't hold the citizenship of that country.
This could be fine inside my mind, but should I suddenly start demanding that others, too, accept this identity, they might ask for some other source of verification such as a passport. If they would do this or not depends on how much my demand to be viewed as, say, French, would encumber their interactions with me or their lives in general.
So there is a spectrum of possible responses to things like transaged people etc:
Everyone would probably refuse to validate an identity which would endanger others (such as me identifying as a brain surgeon when I am not and demanding that others see me as one, too).
Most people would refuse to validate a clearly lunatic identity (such as me identifying as an Elf) unless they just wanted to be kind and couldn't see what the harm in this was (until I kept insisting they learn to speak Elven with me or fly the Elven Liberation flag outside their businesses or set minimum quotas for Elven people in universities).
And most people would refuse to validate a trans-racial identity, at least if the dominant race (white in most places this topic is discussed) wants to identify as some other race.
Friends and spouses and so on probably would validate someone's identity as a great singer (when the person croaks like a frog) if this is important to the person and won't result in attempts to audition at some opera.
So though this slightly depends on the circumstances, when the inner identity conflicts with the rights of others or really consists of demanding that others change most everything in their lives, then we should probably refuse the identity unless it is very strongly supported by external evidence. Even in that case overall numbers of those hurt by this and those benefiting from this should be discussed and used as the basis of the conclusions.