I'm a Discordian Pope and I'll happily give you a certificate stating that it is my sincerely held religious belief that you are hereby exempt from any and all rules and laws that you don't want to apply to you.
I'm not sure why anyone would give such a document much credence however.
A google tells me that Dutch Reformed congregations have some doctrinal objections to vaccinations also, but many have endorsed them anyway. The big surprise for me is that the Jehovah's Witnesses are completely neutral on the issue.
edit:
> The First Church of Christ, Scientist, the publisher of the Monitor, said: “For more than a century, our denomination has counseled respect for public health authorities and conscientious obedience to the laws of the land, including those requiring vaccination. ... We see this as a matter of basic Golden Rule ethics and New Testament love.”
https://www.csmonitor.com/USA/Politics/2021/0920/Vaccine-man...
The way-off-the-deep-end extreme version of this thinking is the SovCit movement, the adherents of which seem to believe, contrary to all sense and evidence, that the right words spoken (or written) in the right order can eliminate the ability of the government to enforce its laws on a given person—that the government is in fact well bound (by whom? Who enforces this?) by some arcane set of well-hidden rules that, if you know how to correctly invoke them, gives you exceptional power over it. As if the government is some kind of rules-bound genie or magic mirror or something. However, weaker versions of this are common. If you've found someone who talks a lot about "technicalities" in legal cases, you're probably dealing with someone who operates under at least a partial misunderstanding of how the law works—that is, they very likely believe that finding little "gotchas" is way more powerful a tactic than it actually is.
I'd be surprised if there aren't a lot of people who think religious exemptions work a lot more broadly than they actually do, and that all you need is to get an ordained minister of some sort to sign off, and that's that, the government has to let you do what you want, and if they don't then that must represent some awful and dangerous break from the norm. Meanwhile, that's not how it works at all.