I don't think any (or not many) Democratic voters are calling for trans to be thrown under the bus. Certainly I am not. I think we need to define what terms like anti-trans or transphobic actually mean.
If a Democrat is punting on or not entirely supportive of government deciding how to weigh in on sports, does that mean they are throwing someone under the bus? Do you think that Democrat may be more or less supportive of trans than any given Republican would be?
I have trans people in my life that I very much fear for, most especially under Republican "leadership". However, if a Democrat isn't giving full-throated support for "men in women's sports", I don't consider that the same as throwing trans under the bus. The candidate may need to evolve on that on particular thing, but then so does most of the American population (75% have reservations about transgender females in women's sports).
The Republicans seem to be very craftily trying to winnow all the many issues out there down to making it all about trans, and then even more narrowly about sports. I don't think Democrats would be wise to let them do that framing. The ones that don't accept this trap I don't consider "anti-trans", either. The Republicans are so very obviously using this one thing to try to blunt what may be a historic blue wave and retain their power, given how unpopular their president is on nearly every issue, including even immigration.
They may be cynical AF in this framing and trying to sow division, but you can be sure that many of their candidates are true believers of the 7MM variety and will be coming for trans (even more) if they get more people into office.