It makes no sense to assume that these guys aren't vaccinated anyway. They aren't against the vaccine, they are against the mandate!
It makes no sense, but the amount of people who conflate the two is shockingly high. I guess strawmans are easier to argue against than someone who holds nuanced views.
edit: one such example of someone who conflates the two https://news.ycombinator.com/item?id=30225017
A couple examples (but there are more):
https://www.bbc.com/news/world-us-canada-52993306
https://www.dailywire.com/news/merriam-webster-suddenly-alte...
LGBT people objected to sexual preference since the 1980s at least.[1]
[1] https://www.chicagotribune.com/news/ct-xpm-1986-07-23-860223...