to corrupt and hijack feminism and steer it towards the right.
It seems to me you're looking at this issue through an American cultural and political lens that doesn't help you understand the legal, cultural and political situation in most European countries. Certainly not the situation in the UK.
Is feminism only feminism if it is leftwing, barleybadminton? And what kind of left? Left-libertarian? Keynesian? Socialist? Communist? Stalinist? Anarchist? The left wrought a history filled with atrocities, too, in case you've forgotten.
And politics across Europe is diverse. Leftwing in one country can be to the right of rightwing in another. For decades, European representative democracies have seen leftwing policies pursued alongside rightwing ones by coalition governments.
And then there's the tendency to hide behind easily adopted leftwing policies that require no effort and cost the government nothing while far more serious issues are never tackled. Malta for instance has horrifically misogynistic laws about abortion, but it embraced self-id with abandon (together with cronyism and some of the worst political corruption). Is Malta leftwing?
Viewed from here, the Democratic Party of the US doesn't even qualify as centre-left, so what exactly are you referring to as "the right"?
And is it your view that women from culturally conservative backgrounds, or women from a centre-right to right wing political affiliation aren't interested in or entitled to women's rights to privacy, dignity or safety? To single-sex hospital wards or carers, to women's sports, to changing rooms or rape crisis counselling? Domestic violence shelters?
The reason why the UK public is increasingly aware and increasingly angry about the political implications of the doctrine of gender identity is because the needs of women for single-sex provisions, sports or spaces have nothing whatsoever to do with our political affiliations. They arise from our biology. And whether they are rightwing or leftwing or anywhere in between, all women share that biology.