Here's the thing

The Church does not teach that anything revealed by God prohibits the use of this vaccine.

The Church does teach that an individual is obligated to follow the dictates of his well-formed conscience.

The Church does not teach that the conscientious decision to refuse a vaccine is impermissible, i.e., that it is not a conclusion reachable by a well-formed conscience.

So there is an opening here. I don't think it's the proper conscientious decision, and it is not by any means a required conclusion, but I can't point to an authoritative Church teaching that precludes it.

It's like (in a limited sense) private revelation. You're not technically obligated to believe that Mary appeared to St. Bernadette at Lourdes, but I'm going to look at you weird if you don't. This guy isn't obligated to believe that the vaccine is morally permissible to receive, but we can certainly look at him weird if he doesn't