The point is that Dems (and Labour/Lib Dems/SNP/Greens here in the UK) consistently frame opposition to GII or support for women's rights as "right wing" or even "far right". Thereby telling anyone who is pro-women or opposed to GII for other reasons to vote for the right. And now the Dems and some people on the UK left are berating US voters because they took the Democrats at their word.
Another thing - the adoption of GII was anti-democratic. Biden's GII-inspired EOs were anti-democratic. They sought to change the law and the Constitution (Titles VII and IX, the right to free speech) by presidential fiat. Not as dramatic as storming the Capitol, but nonetheless... (ETA: What I'm trying to get across is that looked at from a non-tribal perspective, the Democrats are not unambiguously the good guys - Epstein, Hunter Biden, etc)
Everyone has the right to set their own priorities when they vote. Political parties cannot dictate what those priorities are. Bringing Tate back to the USA was not a specific election pledge but abandoning GII was. Voters swung to Trump because of it - voters who would not otherwise have voted Republican.
So I think it is fair to say that the Democrat leadership have to bear responsibility. They made a decision about their priorities - that sticking with their commitment to GII was more important than avoiding the risks a Trump presidency posed. That decision had consequences. They are the ones who should be feeling remorse. But even now, they are doubling down.
Your "abuser" analogy is bad. The proponents of GII - the ACLU, the NCAA, the Democratic leadership - were not "kind". They are the "abusers" of women, children and vulnerable adults. Removing men's privileges, refraining from indulging erroneous beliefs and stopping unnecessary medical and surgical interventions on children and vulnerable adults is not abusive behaviour.