I live in Maine and Democrats here are pretty solid on transgirls in girls' sports. However, I've noticed a bit of wavering. High school sports are a much bigger deal here than they are in the UK - televised on local TV and so on - and also very important for the athletes concerned in college admissions and for scholarships. That makes it particularly galling when a male takes a scholarship that should have gone to a female.
Other states are beginning to see the light, but some are still solid on the trans issue - Illinois in particular, where the governor has a member of his family who is trans, and Washington State and Oregon also spring to mind. I think California is getting to be a bit less gung-ho on the issue, and most of the red states have put a stop to boys in girls' sports (which is one reason so many people think this is a Republican issue).
There is a good book by Kara Dansky called "The Reckoning - how the Democrats and the left betrayed women and girls" , and she writes as a life-long Democrat.
Frankly I can't see why more Democrats who are through the primary process don't come out more solidly against boys in girls' sports - all the polling shows that the great majority of the public would be behind them on that issue, and if those who don't want the vile orange President we have now to keep his iron grip on Congress, who else are they going to vote for?
Speaking for myself, as I have done voluntary work in the women's prison near me, it's the presence of a male inmate who has had (I think) a lawsuit brought against him by three of the women he's banged up with that I find particularly despicable. Look up Andrea Balcer, Maine, if you want the details.