I feel for you OP. My Dnep was very similar. He is ASD and absolutely bought into the big pharma. Insistent that it was all about money for the big companies and we were all being duped.
The first thing that helped is frankly nokne fought him head to head. Everyone on the family communicated that he had every right to his opinion and choice. That surprised him as many of us are in Social Care and health care and all are fully vaccinated with three of us with boosters.
We all meant it thought, ultimately he has bodily autonomy. We did shut down any of the silly comments that we were being duped and insisted on showing us the same respect. There were several times where we were very direct that using derogatory comments about the fact we chose to be vaccinated were unacceptable. Wierdly this all helped as it wasn't an argument. He couldn't get a rise out of anyone.
Honestly it was pure circumstance in the end. DF became very very ill, life threateningly so. Still is and is on an admittedly long end of life pathway. As such my nephew simply couldn't have contact with Df if he remained unvaccinated. Even he recognised the risk was too great. He was never told to be vaccinated he was simply told the acces to Df wasn't safe.
He then chose to get vaccinated. Even a minimal reduction in transmission matters with DF. And ultimately it was DF own choice to protect what time he had left.
So it came down to something he wanted more than his beliefs about the vaccination.
Interestingly recently someone was wittering at him about how the vaccine didn't prevent transmission and he shut them down from a massive height that if DF felt uncomfortable then he had every right to reduce contact with the unvaccinated. He also pointed out that he still believes it should be a choice but no choice comes without consequences. He is more stringent than is now that people shouldn't expect to be unvaccinated and not experience natural consequences.
He's come full circle but he had to get there himself , no amount of pushing from us would have achieved that as frustrating as it is.