That cross-dressing tradition comes from the very opposite direction you’re assuming.

For example in their time Shakespeare’s Plays were entirely played by men, including female roles. This was not because they were very forward thinking about cross-dressing back in 18th century England, it was because it was deemed inappropriate for women to be actors.

It’s a reflection of the so called “Benevolent” Sexism still widely prevalent in those isles, especially in the Middle Class and above - women “are emotional and fragile creatures” and “must be protected” (were do you think the phrase “the gentler sex” comes from?), a paternalist take that justifies denying women access to certain things “to protect them” and certain responsibilities “because they’re too emotional and unlike men can’t handle the stress of such posts”.

You’re seeing the visible, surface artifacts of a society and applying your own values (very likely those of somebody with a high level of formal education and a big city upbringing in one of the most forward thinking areas in America) to try and derive the reason for those things when what you’re looking at is a society which is has been highly calcified socially for centuries, which, except for a bright period after the War that lasted until the 70s, has been dominated in terms of Power and Culturally by a very small section of society whose privileges are passed from generation to generation and were appearances are far more important than action, so with values massively mistatching yours, hence you’re drawing erroneous conclusions.

It’s not cultural openness that drives them, it’s various alive and well streaks of Victorian Values mixed with an unhealthy concern with “keeping up with appearances” (curiously there is a humoristic TV series with that name and tellingly it makes fun of Working Class or Low Middle Class people some whom desperately trying to look higher class, though probably one needs to have lived in that country for a couple of years to read the social context)

The proof that the UK isn’t transphobic is the Monty Python lumberjack bit.

Oh honey.

I wrote a post just above about some self-proclaimed Feminist some years ago with a regular column there writting an Opinion Article in The Guardian about the “evils of men using sex dolls” without noticing how that Perl Clutching Moralizing about peoples sex practices was just a variant of the same thing that was being written a decade or two before about sex between people of the same gender.

I moved to Britain from The Netherlands and the spirit when it came to “accept those different than you” couldn’t be more different between those countries: the Dutch were all about “who am I to judge” and “as long as I don’t have to see it you can do whatever you want”, whilst at least the English (can’t really make informed statements about those from other nations) were all about “if I say certain things it will make me look bad” and “it’s not appropriate to voice criticism of <group>”.

I can’t speak for the past, but at least by the time I got there (mid 00s and for over a decade) the impression of “acceptance” projected by that country wasn’t driven by natural tolerance of others or the cultural repealing of Moralism (I would say, quite the contrary), it was driven by people not wanting to look bad in their social circle.

I’m not at all surprised that such Potemkin Village of “Acceptance” would so easilly collapse.