This is in fact what Russian bot factories are actually doing. And not just around trans activism, but around everything they can use to increase hatred and decrease social cohesion in the west. Here's one source that talks about this problem: https://www.amazon.com/Putins-Trolls-Frontlines-Russias-Information/dp/1632461293
They're doing it pretty well. As a practical example, a lot of the discussion revolving around this topic is powerfully pushing me towards distrusting trans activists, and somewhat towards distrusting trans people in general. There's something deeply irritating about the fundamentalism of it all -- it reminds me of the kind of religiosity that we had to fight against a lot in the 1900s and of course earlier.
I need to remind myself constantly in these threads that trans rights are human rights and that it's the discussion that's fucked, not the people.