Here in the U.S. the more patriarchal political party has been defending single sex leagues and spaces, while the party which enjoys
much more female support is promoting self-i.d. and the like. Possibly things are very different on your side of the pond, but I am skeptical.
Oh, very different. Trust me. Most of the women who are doing the work on this are left-leaning, and absolutely furious with the parties they used to support, used to belong to even, over their refusal to listen and absolute determination to throw women's rights down the toilet.
Even the Conservative politicians who are talking sense are mostly women. Male politicians are either open trans allies or in hiding.
It's not so clear cut in the US. You're both right and both wrong.
Yes, d4m10n, the religious right has been objecting to transgender policies for a long time. But they are objecting for a very different reason, and in a different way, than left-leaning females object. And yes, the Democratic party in the US still has a higher proportion of female supporters than the Republican party has.
But Rolfe is also correct - one of the largest bastions of objection to SELF-ID in the US is coming from left-leaning females.
Feminists are very largely NOT conservatives.
The religious right, which aligns itself with the Republican party at present, has a vested interest in enforcing a patriarchal world view. That view includes a regressive perception of sex-based roles that needs to be able to strictly adhere to social stereotypes of males and females. That view cannot allow for males to dress in stereotypically female attire, because it relies on a strict distinction between the social roles of males and females. This is the view that has resulted in 13 states in the US having completely outlawed abortion of any sort, and which was fundamental in disallowing federal funding to be used to oral contraception. They do not view females as equal participants in society, and thus, they seek to oppose any policies which would further that goal.
Feminists, which align with the Democratic party (but which is rapidly changing), have a vested interest in the liberation of females from the social roles that the religious right seeks to force upon us. We seek the equal participation of females in all aspects of society, and we seek to remove the obstacle of male violence from females, as this is a barrier to our participation. Feminists, however, have no objection to transgender identified people as such. Our objection is to male people invading female safe spaces and overriding the consent and boundaries of females.
That these two extremely different goals find a shallow agreement on one topic is coincidence. It is absolutely not indicative of any actual agreement in sentiment.