"Unsane" was Korzybski's word a long time ago. One blogger in the general-semantics tradition writes: "The difference between unsane and insane is that unsane doesn't necessarily get you into trouble." G.s. uses "unsanity" to mean something like "having a map that doesn't describe the territory accurately."

That said, I think we should recognize that "sanity" is the name of a social, behavioral concept, too. We should be cautious using it, since it may drag in those connotations. A person who can't cope with the world due to psychological difficulties may be labeled "insane" by society even if their map of the world is not any more inaccurate than anyone else's. Once upon a time, being sexually attracted to people of the same sex was considered a matter of insanity; today, being an impulsive child who won't sit still in classrooms is considered a matter of insanity.

Irrational has about the right meaning and has less unfortunate connotations than insane. Though admittedly they might still be worse than what you're looking for.

You want a word that means "these person's ideas are so wrong that they shouldn't even be discussed in polite company".

Look at this from the outside view, you want a word that's essentially a rationalist equivalent to "infidel" without the connotations "infidel" has of making its user seem scarily dogmatic.

There are three relevant sanity levels to compare against: the minimum required to function, the level where most people are, and where we wish most people were. Call these clinical (C), normal (N) and extra-rational (X). If a person's sanity level is R, then

insane: R<C
irrational: R<N
rational: R>=N

It'd be nice to have a good word for N<=R<X, but unfortunately, my intuition says that

unsane: R<<C  

Which would make it an insult; so even if we redefine it as N<=R<W, people who hadn't heard that definition would be likely to react negatively.

It's a band. And a horror film.

Though this may not be the word for it, it's clear what you're getting at, and a word for it may be helpful.

So, do you think this word, "Unsanity" might be worth using?

I expect it is one that I will adopt. Most likely with the 'unsane' word consisting of a link to this post. I always appreciate posts that I can link to in order to minimise how verbose I have to make a comment when trying to cross inferential differences.

So, do you think this word, "Unsanity" might be worth using?

Νο, that looks and sounds like "unsanitary".

If you don't want to use the word "insanity", I'd suggest you use the words "non-sanity" or "irrationality" instead.

EDIT: After a more careful reading of your post, I agree with the "ignorant" and "untaught" suggestions instead.

I tend to support the use of "insane" and "crazy" to mean "severely and systematically irrational", because there are some common points with actual mental illness that makes the analogy reasonable, and the connotations can be desirable. But if you're trying to create a neutral word so that you can put more connotations of badness, irrationality, and irreversibility into "insane", you're going to seriously distort your view of literal insanity. Literal-insane people have lots of experience at basic skepticism, so that's a strong protection against ending up colloquial-insane if you don't fail right at the start. And when you say insanity should be eradicated and use comparisons to vermin, you're saying that you want to take away my pretty hallucinations, and you're begging a reader who doesn't understand the horns effect very well to replace "insanity" with "insane people".

If you want a cutesy word for little problems that aren't so bad, maybe start using "insane" and pick something like "stupid" for the more severe version. Or at least pick something unrelated enough that "insane" will keep sounding like "having reasoning flaws that impair rationality" rather than "so fucked up, man, don't even try".

downvoted for karma begging

The word in-sane is one of many words that is related to the spell of Leviathan. If I am in-sane then I am in sound mind. Period

I like normal-crazy. Crazy has nowhere near the negative connotations of insane and "we're all a little bit crazy (in our own special way)" is something of a meme. "This bit of crazy (you can call it a heuristic if you want) is miscalibrated" has gone down decently for me. The brackets are an alternative, not an aside to say.

Lot of the time the appropriate word is 'stupid', to be honest. H. Sapiens, even the smartest ones, are pretty stupid; barely intelligent enough to have technological progress. Barely intelligent enough to come up with things that make sense, too.