The problem with this is that it assumes Democrats have no agency. Democratic politicians have treated trans issues like those crusty old male Dems who don't like saying the word abortion.
Dems have never provided loud and full-throated support to trans issues. Go watch the recent John Oliver video on trans sports. There are very very good arguments on why excluding trans people from sports is incredibly anti-scientific and just thinly disguised bigotry. But Democratic politicians have never bothered developing the talking points to defend trans people, like they have for other core issues.
Look at how Kamala responded when asked about trans issues. She didn't provide full-throated support to trans people. Her reply was simply, "I'll follow the law."
Democrats have completely failed to defend trans people. They've quietly passed a few state level anti-discrimination laws, but in terms of rhetoric, they've completely ceded the space to conservatives. The only mainstream voices talking about trans issues have been the anti-trans bigots. The Democrats have instead just called the whole issue a distraction and hoped it would all just blow away.
They're right that it is a distraction, an artificial one concocted by Republicans. But that doesn't mean they can just ignore it.
Propaganda works. And if you don't do the hard rhetorical work to fight it, it eventually does change public opinion.