Republicans over 50 go to church, and churches are massive drivers of vaccine promotion and awareness outside cities. This applies worldwide, even to issues other than COVID (Catholic outreach in certain countries is the only reason the locals trust any medication at all) but also in the United States in specific. Hospital/church partnerships are common in the South especially.
Christian opposition to vaccines and medicine in general comes from online sources or lone TV "priests" with paid audiences; services that are, at the end of the day, fringe.
On its coattails, COVID has catapulted generic anti-medicine beliefs from a very niche bipartisan affair most prevalent in elderly individuals with "alternative lifestyles" (hippies, rich people, and Christian communes), to a much more prevalent but skewed young, male, Republican-leaning demographic. No longer is taking water pills and huffing essential oils to ward off Satan the exclusive domain of Californians and over-eighties, now your plumber thinks it's cool too!
That demographic happens to be the one absenting Sunday services because it was too preachy for them, which is a major and current concern of most religious bodies in the US. Entirely coincidental, I'm sure.