I don’t believe that most politicians of either party actually give a fuck about women’s sports in general - they certainly never have before this issue came up. For cowardly democrats on the anti-trans side of the sports issue, they simply see this as a way to avoid appearing too “woke” to independents and conservative democrats, while only directly affecting the handful of mtf athletes among their constituents.
I fully agree that most trans folk and their loved ones would gladly cede the sports issue in exchange for some real protections - I certainly would.
I’m not saying that these anti-trans democrats are trustworthy; I’m saying they are motivated by poll numbers, not personal animosity. Losing won’t motivate them to do better unless they lose to someone with better values - that’s why we can teach them lessons in the primaries but not in the general election. If they lose in the general, the lesson they will take is that they weren’t conservative enough, so withholding your vote at that point is counter-productive.
The republicans want to pass bills that will make life overtly harder for trans folk, beyond sports and even bathroom use. The priority right now is to take away their majorities in the House and Senate, so that those bills can’t even be brought to the floor for a vote. Beyond that we have to hold them accountable during their term, and we can primary them next time around. There is no situation in which withholding votes from Democrats in the general results in better outcomes for trans people.