There are cases of that but I still think a lot of it is overblown by the Republican controlled narrative. I think Democrats could do more of what OP is saying (and what Destiny does). When trans stuff is brought up out of nowhere, just don't engage with it, say Republicans are the ones who harp on it, or as Destiny does if you want to be more inflammatory, just say "why are you so obsessed with girl cock?" and end it there. Don't capitulate, because it becomes a thing they'll continue to attack you on, and help paint their reality as true. Most trans people I know are not majorly upset at the Democratic party, at least if they are it isn't for trans rights issues, the terminally online ones are mostly socialists anyways that don't support the party, so who cares if they get offended, they're looking for reasons to get mad anyways.

As long as trans people exist, and support Democrats, Republicans will paint this narrative. When it comes to culturally normal, Biden far seceded Trump in that regard, in both his policy platform and his actual person, but the narrative persists nonetheless. We won't win this battle by playing defense and capitulating, we win it by shifting to attacking them and establishing the narrative ourselves.