If this is accurate (which is a big if, and I'm asking the question to try to figure out if it is) then we could make a lot of progress in trans acceptance very quickly by just reframing the whole thing in these terms.
The woman-in-a-man's-body concept sounds mystical and metaphysical in a way that triggers religious objections from substantial portions of the US population, even those in the middle politically. But arguing that males shouldn't need to live up to an artificial and incredibly outdated standard of masculinity? That would be a much, much easier sell.
So I guess the followup to my question is: if for most trans people it is cultural and not biological, why are we doubling down on gender binaries and talking about switching genders instead of creating a campaign that would both get at the root of the issue and be easier to swallow for a larger portion of the country?
(I say this fully aware that biological intersex is a thing, but from what I understand most trans people are not biologically intersex in any measurable way. Correct me if I'm wrong.)