Mike, I’d wager there are more religously conservative Muslims in the UK now than there are trans people – so in a multicultural society they wont come at the bottom of the list in terms of being provided for.
“We shouldn’t make sensible provision for trans people because the Muslims wouldn’t like it” manages to be insulting to both trans people and Muslims.
I know plenty of religiously conservative Muslims. Funnily enough, they have no problem whatsoever with working and socialising with gay people, Jews, Christians, or any other social group whom Muslims are “supposed” to hate. Most people, from any background, are decent and tolerant.
On a practical note, for cultural reasons to do with modesty, the Muslim men at my gym tend to use the cubicles for changing anyway, whereas the non-Muslims use the communal areas and let it all hang out. If a trans person were to come in and change, I doubt any “conservative Muslim” would even notice. Nor, I’m sure, would anyone else.
But yes, there will always be a vocal minority of extremists who oppose tolerance and equality. And the rest of society, rightly, ignores them.