I don't see it. All appropriate qualifications about how it's still very close to the election and we're still gathering data etc. aside, one thing that's very clear is that Harris did better in the swing states relative to the rest of the country. This means that where she campaigned and where he campaigned, he underperformed. Those were the states blanketed with the most anti-trans advertising and it clearly didn't help him; if anything it seems to have hurt him.
A somewhat different argument that I think could have more merit is that trans issues plus other cultural issues (DEI, etc. like you note), while not individually salient, contributed to a diffuse feeling all across the country that Dems don't really care about "you" (whoever "you" happens to be). But Democratic candidates can't help fight that by ducking the culture war issues; they already do that and it's that ducking that contributes to that very feeling among many people.
The basic approach needs to be a commitment to egalitarianism. Egalitarianism as a concept is very popular and defending women, minorities, and gay and trans people as part of the fight for egalitarianism against the billionaires trying to divide us so they can treat us all like chattel should not be a hard message to sell.