I would argue that no identity is a fact. All identities are beliefs on the part of the person doing the identifying. To identify something as X is to express the belief that it is X.
This reminds me a class very long ago, when the teacher wrote two contradictory definitions of style in the blackboard, one saying that style is what the authors have in common with their school, the other saying that style is what the authors have that others don't.
Of course, those were defining two different concepts: the style of a school and the personal style.
To be precise, identity is very easy to define: it's to be you, instead of anyone else. Until someone invents some kind of brain trasplant, it's impossible to transfer consciousness, so your identity is your body, more specifically, your brain. That would include your memories that, although can be erased by trauma or illness, are mostly very strongly rooted.
Outwards, it would expand to your habits, your chemistry, your beliefs. All that can change, but it's difficult. So it's more your personality than your identity.
Then there is "identity" that isn't. More like being part of a group, so it's parallel situation to that of style. You identify yourself with a group, you define yourself as the sum of the groups you include yourself in. Identity is very much about individuality. "Identity" seems to be the opposite: the inabilty to be someone on your own.
Unless we're getting to some deep metaphysical stuff, I don't think I buy that. Yes, some identities are solely based on belief. But others are indeed based on facts: someone might identify as "basketball player" because they play basketball. Or they might identify as "tall" because they are in the top 10% of people for height. The height example might sound silly, but there are people who are somehow "proud" of these sorts of traits that they have no control over.
Certainly the situations can sometimes change: the basketball player might stop playing basketball and no longer identify as such. And I suppose someone who has never played basketball in their life could adopt the identity of "basketball player" if they wanted to, but... that's fine, that would be a case where that particular person's identity is based on a belief (or delusion).
I'm not talking about what the identity is based on. I'm talking about what the identity itself is. I think this is useful to help clarify the difference between "X has the identity Y" and "X is Y" which otherwise seem very similar. The former means that "someone believes (or many people believe) that X is Y".
Literally anyone can be Christian, but that doesn't make it a useless tag. It's a linguistic and mental shortcut that has utility despite the relative ease of application.
Non-binary people can be queer, heterosexual trans people can be queer, asexual people can be queer. Same with polyamorous people.