The US situation seems to me to be far more tribal in terms of politics than the various UK settings (England, Wales, Scotland, NI, all slightly different imo). The extremes are their own tribes, and if one side states that water is wet the other side will start a foundation to sell desiccated water. In other words, it is almost impossible to have an actual political debate across the tremendous political chasm.
I believe the right began the process of turning much more extreme, in fact so extreme that the far right is now entirely undemocratic and authoritarian. It is also a men's rights movement.
So even though the left has now also become authoritarian and woman-erasing, it is extremely difficult for lefty women in the US to be openly gender critical as the right is doing that.
Never mind that the reasons for opposing the gender identity ideology are diametrically opposed (the right needs women to be the sex they wish to control and keep submissive as a resource, gc feminism wants women to be the name for the female sex so that the right's attempts can be fought against and sexism and misogyny and sexual violence and sex discrimination addressed): Anyone openly criticising the concept of abstract gender identities as the proper replacement for biological sex in everything is assumed to be a right-winger and a bigot.
This means that turning this particular ship will take much more time here than in most European countries, if it can be turned, and what happened to Roe makes this even harder as gender critical women now have no place in politics which would support traditional women's rights.