Browsing his personal website reveals frequent mistakes in science, statistics, and probability theory. I don’t think I’ll spend any time on this paper.

Well, the "article" is mostly an opinion piece, it could as well be a Twitter thread. So, at least, there is some value when evaluating a personal opinion in the context of other opinions expressed publicly by the author. I'm not saying this is the case, but I don't think is invalid either.

Of course it’s invalid. Either there is something about the substance of the article that is debatable or there isn’t. Other opinions are completely irrelevant.

If I write an article about the benefits of X drug and have expressed publicly by other channels my support for the company that produces such drug, I think is relevant for the discussion of the article I just wrote. That's why I said that may be it is not the case here, as I my self don't see any relationship between the linked tweets and the article. But I don't think is to crazy to think that two related opinions can be analyzed together regardless of the channels of distribution.

If you write an article about the benefits of X drug, you have presumably made arguments that can or can not be supported with available evidence. Your other interactions with the company producing the drug are irrelevant.

That's not very Bayesian of you.

You need to review your understanding of Bayesian statistics then

It is not just his beliefs it is also how he seems to get fooled by Russian tabloid style fake news.

This subjective logic can be applied to every person that's ever lived.