Right, like in this context it's just being. The 'identity' part of gender identity seems like a really unfortunate misnomer, or maybe not misnomer but something very specifically defined differently than the way it may be more commonly used. I just read this old paper from 1977 wherein the author attempts to define it:

masculinity and femininity represent two ends of a distribution, and they refer to this distribution as gender identity. Gender identity, then, refers to the self-awareness of one's role as either a man or a woman and is apparent in everything a person does to indicate that he or she is male or female.

The important point here is that we are not considering masculinity or femininity as unitary concepts. but rather as characteristics which a person may have varying amounts of. Also, gender identity includes a wide range of behaviors, besides sexual preferences.

The concept seems like just an attempt at interpretation to explain behavior, not what or who a person actually is, even if they believe they are the other sex (or species or race or nationality or whatever else a person may 'identify' as). A person could think of themselves in a certain way, but that seems like a different kind of identity than some (un)official identity.

It might sound jaded but I don’t take anybody at their word on anything, really. People are constantly showing us what they really believe and it’s often at odds with what they say. Seems to be more true of large groups.

I don't think that sounds jaded at all, I think that's a natural way to protect oneself. 'Actions speak louder than words' and it seems easiest to catch people lying when their actions eventually betray their words. That's interesting you note that commonly amongst large groups, I hadn't noticed that but definitely something like religious groups or governmental authorities seems to definitely display that.