BUT. There is a world of difference between a 'no' that comes from a place of, "I don't give a shit about your struggles" and a no that comes from a place of careful thought and compassion for all, even if the immediate conclusion is the same.
But that's not the usual response to questions about how trans people should be able to exist in the world safely and with some dignity. Not women's problem is the usual reply. (not specificlly replying to you with the following but the thread more generally)
The left has a long history of splintering off and going in dubious directons - it's one of the reasons anti-semitism became such a problem. And sadly I've lost more than one friend to conspiracy theories in the last few years.
There were certainly many in the left once who considered themselves perfectly decent progressive people who were opposed to lesbian and gay rights, often because it was something they couldn't empathise with, it made them a bit uncomfortable, they felt it was somehow anti-science and that it represented a theat to children. Had the internet existed in the 80s, and every time a gay person committed an awful crime or said something stupid on social media it was shared by tens of thousands of people, I can well imagine a more militant homophobic movement from across the political spectrum would have emerged.
I think comments I see about how people have 'peaked' or 'woken up' and now things can never be the same again are very revealing. That is the language of conspiracy theorists and suggests a coignitive shift away from the very complex and necessary analysis of the range of factors involved in social change to a much more simplistic one which involves secret plotters behind the scenes. So if an organisation is pro-trans rights it's never because of shifting social attitudes towards LGBT people, combined with the fact they might have a few trans employees they want to support, or they might even lean in a different direction on some of the arguments, or might just want a bit of trendy PR. No, they've been 'captured' by Stonewall. It's always presented as devious plotters behind the scenes whether that's the morid claims of trans Jewish billionaires planning a trans-human take over to more mundane insistance that the local library has been 'captured' by TRAs who are using Drag Queen Story Time to further some insidious agenda.
None of this is how social change works, there are no secretive TRAs running round switching the word sex to gender on forms, there is no organised plot to invade women's spaces, there are just trans people trying to find a way through this muddle and living their lives, and activists, some good, some shouty arseholes like in all political movements and a few charities who carry out the kind of lobbying for their interests that every other charity does. And slowly, with bumps in the road, trans rights have progressed. To claim shadowy malign (usually lefty) actors with untold power behind the scenes is a right wing, conspiratorial analysis - for an example go on a landlord forum after the government has done something perceived as positive for tenants and you'll find landlords ranting about how the homelessness charity Shelter has captured the government and that they now hate landlords and want to destroy them.
And I think the problem is once someone peaks, or red pills, or sees the light, then it becomes an obsession, it becomes all someone can think about and they have an urgent need to spread this secret knowledge they now possess, to evangelicize. At this point anything which strengthens the conspiratorial analysis will be embraced and anything which questions it fiercely rejected.
At this point objectivity has gone out the window, and it's why someone previously of the left can say well on this matter the Daily Mail are really rather sensible. The Daily Mail write about trans people in exactly the same way they attack all other marginalised groups - it's not like some magic ethical mist descends on the news room every time someone writes about trans people. Every single word they write is designed to make you frightened of trans people and angry about trans rights - if you've lost the ability to analyse that, even if you might agree with some of it, then you've lost objectivity.
Of course the constant evangelicizing won't work because most people haven't undergone this coignitive shift and so 99% of people will be like yeah what ev's because they've got more important things to worry about and are sick of someone going on about trans people all the time. But some people will get drawn in, sometimes vulnerable people but often highly intelligent educated people, especially at a time of widespread social unease when we're all a bit wobbly anyway and so it spreads, becoming stronger with every new recruit. I remember when David Icke could barely get a book published, now he can sell out Wembley Arena and his audience is full of educated intelligent and often formely quite lefty people who've gone sideways after their own experience of 'peaking'.