It's a slightly daft way of saying what they mean, given that 'self-identify' now often means 'claim to be something you objectively are not'.
Well, to be fair, we tend to think of it like that, but more formally it's "claim to be something you may or may not be".
Except that sometimes they don't really mean that, they do actually want you to be as well as claim to be. (But why they want to exclude people who are but claim not to be? 
)
It's the same as obfuscating and saying something is for "people assigned female at birth", when no, that's almost always not the relevant factor, it's whether you ARE female. If you were wrongly "assigned female", but turned out to be male, then it wouldn't apply to you. And if you weren't assigned anything at birth but are female nonetheless, it still applies to you. The ancient paperwork is not what matters, it's your actual sex.
I think its clear what BC think overall on this topic!
Yes, that's clearly it. It's "in-group" jargon being used to signal that they're part of the bourgeoisie, regardless of impact on the people they're allegedly trying to communicate to.
They're saying the words without even fully thinking about why they're saying them, but they know that those are the Words That You Say.