Board members at Southwest District Health, outside of Boise, questioned the vaccine’s safety during their Oct. 22 meeting and narrowly voted to stop providing the shot in the six counties they serve.
Health departments in Texas, Florida and Michigan that led vaccination campaigns in their communities at the height of the pandemic have also pushed back against the COVID-19 vaccine.
Last year, Texas policymakers banned health departments and other organizations funded by the state government from using funds to promote their vaccination efforts.
The Florida Department of Health issued guidance in September warning Floridians not to get mRNA COVID-19 shots after Joseph Ladapo, the state's surgeon general, recommended people avoid them in 2023.
In Michigan, commissioners in Ottawa County turned down a $900,000 grant for their health department in September. Joe Moss, chair of the commission, said at the time he was “opposed to accepting any COVID grants,” according to the The Holland Sentinel. The revised budget came a year after threats to slash funding sparked local protests.
This is a deeply unserious country. 
Is there a materialist reason why Chuds are anti-vax, or is it just brainworms?
It's because their media made it a culture war issue during the height of COVID.
Capitalists wanted to cut all COVID aid (wouldn't want the proles getting ideas) and manufacture the end of the pandemic so that people went back to work ASAP. To do this, they have to convince people that COVID is not a threat, because actually dealing with COVID would take too long (and might give those proles those ideas). So the billionaires who own all of the media in the country (and the world, for that matter) start a non-stop broad spectrum propaganda campaign about why you should stop worrying about COVID and go back to Applebee's. Anti-vax, anti-mask, anti-lockdown, etc messaging is shot out of a firehose directly into the chud brainstem by a half-dozen media networks.
Chuds are anti-vaxx because they have to be convinced to fight against their interests somehow and anti-vaxx conspiracies are part of how this is sold to them.
The GOP and far right explicitly push an anti-worker agenda and an anti-social spending agwnda, things that are aligned with ruling class interests and against the interests of the vast majority of chuds.
So to sell these ideas, which would otherwise be impossible, the American right has created a deep alternate reality universe of false consciousness for them to dive into. As another commenter said, the culture war. One of those pieces of lore is to be "anti-government", which is where much of the anti-vaxx sentiment comes from, of saying there are various government conspiracies and it's government backed so don't trust it. Obviously this is selective reasoning because chuds also worship the US military. Keeping chuds locked into anti-government conspiracies keeps them docile and in line with the deconstruction of social spending, degulation, and lower corporate taxes / whatever capital wants to do.
In terms of direct material reasons around COVID vaccines in particular, that's a funny one because Trump was very pro-vaccine and this threw their cognitive dissonance into overdrive. They were more organized around anti-masking and anti-lockdowns. But they had already had this anti-vaxx contingent for years and years and so they kept trying to figure out how to square this with their knee-jerk support for Trump.
The election of Biden made this easier, as you couldn't call it "the Trump vaccine" despite him pushing for it and wanting all of the credit. Trump supporters could just refuse to take Biden's vaccine, they don't trust him or the government, don't put that poison and microchips in my veins. These are people who refused to mask, already had COVID twice and didn't die, and were saying it was just the flu.
So, more proximally to COVID, I will also confirm what others have said and tie this to capital's interest in forcing people back to work and in nirmslizing COVID, which ends up with a hilarious and morbid contradiction, which is that the main push and tool for normalization was vaccine-based, the vaccine was meant to get people "back to work" and cut benefits, but the overall push to normalize had vaccination as a casualty, as people were able to slot it back into their previous anti-vaxx theories.
communism is when the government does stuff (vaccine campaigns). /jk
but seriously, i would gamble that the general public has been primed to be distrustful of the government because of all its fuckery and capitalism exploitation with neoliberalism. top that with the corporations and their running dogs/lackeys wanting no covid precautions/fear because it affects revenue when people are taking precautions because of disease, (so they produce anti disease intervention propaganda).
the entire economy runs on treats and buying random shit, so staying home and avoiding going out is bad for business, so the petite bourgeoisie are interested in reproducing this propaganda, and i would gamble most chuds are of this class if not labour aristocrats
i think julia doubleday is some kind of marxist, check out her substack for more materialist orientated analysis (though i don't think it is explicit, since i think she is doing the whole crypto-marxist to get her work out)
I really wonder if the chuds would be anti vax if Trump won in 2020. It seems like the libs wouldve taken the antivax mantle for a little bit.