Short version: the issue with "reality is normal" is that the English statement looks bidirectional when the concept is actually unidirectional assignment. That is, a CS way of stating it would be:

normal := reality

This is, as you say, the solution to a lot of philosophical panic. The reverse statement

reality := normal (wrong!)

leads to a lot of confusion, and it's unfortunate that "reality is normal" doesn't exclude that interpretation, because this can lead to the double illusion of transparency. It looks to me like this post is valuable because it highlights that risk and tries to counteract it.

I'm not sure that your attempt to counteract it is very effective, though. When I first read the phrase "reality is weirdly normal," I thought you had totally missed the point. To quote from Think Like Reality:

Whenever I hear someone describe quantum physics as "weird" - whenever I hear someone bewailing the mysterious effects of observation on the observed, or the bizarre existence of nonlocal correlations, or the incredible impossibility of knowing position and momentum at the same time - then I think to myself: This person will never understand physics no matter how many books they read.

Perhaps "reality is unintuitively normal" is closer to what you were trying to say- but again the issue is that you want reality to be intuitively normal. That's what it means to understand that part of reality. For humans, it takes work to align your intuition with reality but it can be done, and so something like:

reality := unintuitive (wrong!)

seems like it actively disallows that possibility (and tries to have the map influence the territory).

In the third maxim, what's "normal" is the universe as humanity sees it — though this still doesn't identify normality with what's believed or expected.

I'm not sure I agree with this interpretation. To go with the wiki's explanation:

The purpose of a theory is to add up to observed reality, rather than something else.

If by "as humanity sees it" you mean "observed reality," okay, but "as humanity sees it" seems very prone to the other interpretations you want to exclude. "Observed reality" seems to exclude them, and also to concord nicely with the demonic view.

I think the rest of the post does a good job of highlighting and dispelling various confusions one could have about this concept, and I think banishing confusions is a very important part of education and communication.