I don't think that's true. I work closely with a lot of different families in my job, and due to the demographics of my job, we get a reasonable section of anti-vaxxers. Most of them you wouldn't be able to pull out of a lineup. They care about their kids, they contribute to their communities, and they're just trying to get through whatever challenges they have to get through each day.

I would put the root causes as distrust and fear. Distrust of government, systems, the media, etc. and fear of what they don't understand, so they look for some explanations that align with their emotions.

So, for instance, vaccines hurt, don't make sense (they don't understand the science), and make their kids cry, so they're very emotionally invested in not liking them. Then anyone confirming their distrust and supporting their emotions will easily sway them, so they swallow anti-vaxx messages whole.

Same thing for anti 2SLGBTQ+ sentiment; they think trans people are "icky", have an emotional response to it, and are then primed for any conspiracy theory that confirms their distrust of the system (education system, in this case) and gives them an excuse to justify their emotional response. It resolves their cognitive dissonance.