Partly true, I would say. The Democrats suck at messaging, but whenever someone uses the trans issue as their go-to example, I get a bit suspicious. Which Democrat is out there saying what the Republicans are accusing them of? There isn't one. It's just the Republicans lying really effectively.
I watched an interview with one of the candidates for DNC Chair on the Pod Save America podcast, and he made some interesting points about how the Democratic party fails to communicate in unison. Like for instance how Biden walking the picket line with the UAW became seen as a Biden action rather than a Democratic party thing, because they don't pick it up and message on that effectively.