The question (you know this, of course, I'm just trying to get it clear) is a subordinate question to that involved in the well-known mind/body problem ('mbp'): how do (non-material) minds relate/interact (causally and otherwise) with (material) bodies?
Given the assumed possibility of 'matching', trans metaphysics has to take it that minds and bodies, although different in certain ways, are nevertheless the same sort of thing. But this, now, constrains the solution-space of the mbp.
Generally, the trans metaphysician has to say one of three things about mind/body interaction: it's a miracle ('God does it'); mental things reduce to physical things; physical things reduce to mental things. Generally she doesn't want to say any of those; the question you pose, then, remains, not just unanswered, but unanswerable.
A more promising line with mbp (given we don't like any of those three answers), is to deny that minds and bodies are the same sort of thing. Gilbert Ryle, for instance, in castigating what he called the 'myth' of the 'ghost in the machine', described the mistake involved in thinking minds and bodies are the same sort of thing as a 'category error', a locution which has become relatively mainstream. (That's in his Concept of Mind, of course, though not exclusively.)
Others have made similar moves. I mentioned David Hume in an earlier post. Buddhism has an interesting, some would say similar, take on mbp. And so on.
OK, that all needs further explanation. This is not the place. But two things strike here:
- If minds and bodies are not within a single category, it is difficult - say nonsensical - to think of matching them one with another. So trans metaphysics collapses.
- The important thing here is not so much that trans metaphysics is wrong (although it is); the important thing is that it is debatable. Given the possibility of error, and the fact of disagreement, it would be crazily unreasonable to base public policy on such grounds. We should not, that is, allow trans metaphysics, or the policies it claims to underpin, into any part of our public weal.
So, in short, those who believe in matching minds to bodies should be left to their own devices and not allowed any group influence in public policy or public institutions such as schools and healthcare services. Such a bar is of course well possible without discrimination or any kind of 'phobic' outcome: it is a policy well established for other different metaphysical, philosophical and religious groupings of believers.
LG and B? Different, of course. We have every reason to accept LGB concerns into deliberation on public policy. Just not T, for the reasons I have outlined.