Citation needed! Pretty sure you do not have an accurate bead on how "everyone" reacted.
My guess? When people read their trusted news source, and it disagrees with a previous assertion that they've bought into? "Ugh stupid opponents are infiltrating our news. No way I'm buying into this government bullshit trying to force vaccines on us!"
(But I hope that what you say is right - that conservative news is finally encouraging vaccines... and maybe in a few weeks/months their audience will subconsciously flip to "oh yeah vaccines are good. I've always been planning to get them but I needed some assurance they are safe, which we're finally getting just now.")
That's not the same as being anti-vax if the vaccine was allowed to follow the original timeframe for development and testing (which it eventually was).
https://www.vanityfair.com/news/2021/07/whats-behind-fox-new...
I don't know the reaction among Fox News' viewers. It'll be interesting to see if vaccination rates tick up markedly in red districts.
My suspicion is that it's some of each, and I'd bet that the numbers in red districts will rise some, but not a lot. Proportional to the ~2 million Fox News viewers, out of ~80 million people who voted Republican last time. Not that all Fox News viewers will rush out to be vaccinated, but that [say] 25% of them will and influence an equivalent number of non-viewers.
Pulling those numbers out of my ass, of course.
As a current example, in the United States the Republican party has been against vaccines. And have been telling their base to doubt them or not get them. Fox news has lead the way along with lots of other media channels.
But for some reason they changed this week and started claiming everyone needs a vaccine. So the complete opposite story. And no one batted an eye.
It is like living in 1984 to a degree. So weird.