I didn't make that suggestion. We've been discussing that original point throughout. If you want to step back and acknowledge that academia doesn't control the population while still insisting that the media does, that would be helpful.
I don't see the analytic value of separating Fox. In total, the media was very supportive of vaccines. People who are inclined to seek out partisan media had partisan takes--which *at least* suggests a possible problem with your argument that you should address and consider. Specifically, it lines up with the theory that people seek out media that tells them what they want to hear better than the theory that people are "controlled" by the media.
What are you trying to say here? The power of Fox's propaganda also forced non-rightists into being anti-vaxxers?
This is an argument from (imagined) authority as well as a circular argument (it's true because it's a fact, and it's a fact because I say the authorities say it is).
Well, I recommended a book that lays out the case and cites a lot of data. Pointing you in the direction of data isn't cherry-picking.
Did you read that? What they conclude is that showing a visual stimulus "subliminally" (defined) probably can cause a neurological response (e.g., a flash of an angry face could slightly cause arousal even if you don't notice it). It's a very weak effect (much less than, say, a frowning person getting in your face). That's why I said it depends how you define "works." Subliminal messaging isn't going to drive your decisions, and to the extent it has any effect at all, it's much weaker than more obvious stimulus.
Again, not a meta analysis. The reason I point that out is that in psychological studies particularly, you can find all sorts of crazy effects in any particular study, and then they don't replicate. There are lots of websites devoted to that. I think a single study is useful for identifying a potential effect to look into, but it's not going to be the last word on anything. And when you have an issue that gets studied a lot, that's particularly a problem. Also an issue in health studies (e.g., you'll find lots of health studies showing that homeopathic medicine works, even though there is no plausible mechanism by which it does, and meta analysis doesn't support it). "Subliminal messaging" is on a level with homeopathic medicine.