“religious level of faith” implies there is not a mountain of publicly accessible evidence showing vaccines are safe and effective, and that instead these people’s beliefs are neither provable nor refutable.

I know of no other reasonable definition of religious beliefs.

It's a lot simpler than that. The point of the argument is that some people take the word of these companies without questioning that there might be an alternative motive that doesn't take their safety into account. This would be a "religious level of faith" as it implies a dogmatic adherence to what some person is saying.

It has nothing to do with believing vaccines work. It's simply taking things they say with a grain of salt because capitalist forces often encourage them to do the wrong thing.