How can you possibly find the group that represents the intersection of both 'covid is no big deal and I'll continue to live my life as normal' and 'you should take the covid vaccine'? This is like trying to find a pro life obstetrician who performs abortion. Other than the mentally ill, no one holds those two beliefs honestly at the same time. If it does exist, it probably doesn't in numbers large enough to matter.

We are approaching the limits of empiricism.

Double blind technique should eliminate a lot of these confounders, eg if you don’t know whether or not you’ve received the vaccine, your behavior presumably wouldn’t change much. However that is admittedly harder with the MRNA vaccines since most people have some mild side effects after the second dose.

Those distrustful of vaccination are unlikely to sign up for trials

Or are the trials being conducted clandestinely?