Nonsane would be better, I think. Whereas unsane suggests a strongly opposite to sane, nonsane suggests a mere lack of sanity.
I'm shocked that this ended up in an extreme upward spiral. "Strongly opposite" doesn't seem to be the suggestion at all. We have an actual word (insane) that means that and the fact that someone has clearly gone out of their way to use insane is an overwhelmingly strong indication that they are not trying to say "strongly opposite to sane!"
The difference between "non-X" and "unX" tends to be that 'unX' is closer to being consolidated into a single word than 'non-X' which is closer to a word with an external operator applied. Kind of like 'atheist' vs 'non-theist'. Real words that are actually words tend to be 'unX' and not 'nonX' (typing nonchristian into google just gives you a suggestion to try 'non christian' which in turn returns results consisting 'non-christian') so creating a fake word of the type 'nonX' is just totally unnatural.
The above is not to say that 'unsane' should be used as alternative to using 'sane' with a 'non' operator. Just that having my tribe adopt a 'nonsane' as a jargon word would be outright embarassing. It's nerdy while not even having the saving grace of doing nerdy right!
Edit :Excellent suggestions in the comments. Two of them stood out for me:
We often use "insane" to describe people whose behaviour or beliefs are below the sanity waterline. But as most must would agree here, you cannot call someone insane with a straight face just because he happens to believe in magic.
I'm currently watching Future by Design, a documentary featuring Jacque Fresco and the Venus Project. Jacque came up with this word, "unsane", to describe people who basically, aren't rational because they haven't been exposed to the right ideas yet. Which would be different from "insane", which is more about irrevocably irrational people.
I like this word, because there isn't the tone of accusation we find in "insane". This neutrality makes it easier to say that we can do something about it. Insanity should be eradicated like vermin. Unsanty on the other hand can be fixed.
So, do you think this word, "Unsanity" might be worth using?