Snappity
Your first two examples are about people living abroad and how to acknowledge that in the UK. I don't really understand why that justifies a system of self-declaration, instead of (for example) making the admission of medical evidence from abroad a clearer process. I'd also assume that in the second example - if the asylum claim is made solely on the basis of transsexual identity then clearly that should be noted in the immigration paperwork just as if someone was escaping another form of persecution. I am a little confused as to why the person born abroad should need to amend a birth certificate, presumably issued from their country of origin, for this process? Wouldn't the mismatch between their birth certificate and their physical appearance +/- medical paperwork form Exhibit A for their asylum claim? Additionally, I thought they'd be treated as their preferred gender as a matter of course, as I've been informed on by trans activists repeatedly.
As to changing birth certificates, try getting visas for some countries if you can't get all your documents matched.
I've never had to show more than my passport for visas, which I understand can be changed for a fee with relative ease. But certainly for some places you might need more documentation. This sounds like a case for the diplomats, though, because they should do something about keeping citizens abroad safe.
How about insurance? If the form says sex and you haven't got your birth certificate changed, the insurance might be invalid - and nobody should have to to out themselves to get motor insurance. Or drawing a pension from an occupational pension scheme - they often demand birth certificates. And without changing a birth certificate, there is no right not to be outed by a malicious official without being able to rely upon s22.
This last part of your post is interesting because we've been fed the line that the birth certificate doesn't matter, trans people have all their practical rights anyways, and sex based rights aren't going anywhere. Are you admitting now that actually having a GRC/Amended birth certificate does impact legally on the determining of someone's sex? And therefore women should be concerned about making this process easier and open to all with no gatekeeping?