I have been thinking about this for quite a while. So thankfully this showed up here. I have my own take on the matter, that you can enjoy, or not.
For me, the basic question in my relationships with others is not about what I am, but about what we are doing. Or, more directly, what rule set we are operating under. All of our social interactions are covered by a gigantic web of tacit social rules, that, while unstated, are still enforced, one way or another.
For example, imagine responding to the friendly comment about the weather from the cashier at your local supermarket with more than a casual "oh, its going to be a nice weekend". Stretch that out into 20, 30 seconds of personal disclosure about what you plan to do, and watch people waiting in line, and the cashier, start to shift and act nervous. Even if there aren't people in line, see how long it takes the cashier to start commencing the friendly brush-offs. But don't do this experiment, because that would be rude. We have many rules about what and is not appropriate in conversation, personal expression, body language... but none of these rules are exactly written down, but we still have to follow them.
A good way to say this as that as much as identity might seem to be a question, the more pressing issue in our interactions is roles. We are expected to act within the constraints of a role, and failure to do so can bring down sanction, from the mild annoyance of strangers to quite serious legal problems.
Many of our rules about roles and norms relate to gender expression and interaction. I am a man, and there are many tacit rules about how I can socialize and communicate with women, even in seemingly innocuous situations. I have male friends, such as Qousqous, that I can bombard with non-sequitur messages throughout the day, posing hypotheticals to him about Navassa Island. In general, I have found that even when I have a friendly relationship with a woman, that too much communication can be annoying, even harassing. Our society has rules about the roles we play, and even in our era of confessional internet, there is still such a thing as bombarding someone with TMI and inanities.
Which is one reason that I think the pronoun question is, if not silly, very inadequate. I have friends (and have even had one romantic relationship) with someone who now identifies, and acts, as a different gender. But. Often the tacit rule set of how we interact was set up over decades of interaction. Despite the stated shift in identity, I am not sure how much the rules have changed. Someone who I established a relationship with as a woman is now non-binary, but when they are "busy", I still treat it like when a woman is "busy"---a friendly way to tell me she is only interested in superficial interactions. And when someone who I established a relationship with as a man is now a woman, I still think it within the realms of appropriateness to random chatter to them about my favorite animes. And when a person who I had a (admittedly brief and odd) romantic relationship with when they are a woman is now non-binary and tells me they don't wish to talk---I treat that as an ex-girlfriend saying that, not as if it was a male friend saying it. (So I am, in effect, disrespecting their gender identity by respecting their wishes.)
Do you need an identity? Your identity is a shiny, ephemeral ghost in the machine that can only be known to you after communion with the Vorlons. But your role? You require one of those, and if you are uncertain of it, grit will start piling up in the gears of social interaction.