Near-universally applicable alternative to "sanity check"

Consider, coherence check and confidence check.

coherence: systematic or logical connection or consistency M-W

consistency: agreement or harmony of parts or features to one another or a whole. M-W

confidence: faith or belief that one will act in a right, proper, or effective way M-W

I'll suggest a 'soundness' check, or 'soundness scan' if the check is superficial:

soundness, noun
The condition of being free from defects or flaws.

(soundness. (n.d.) American Heritage® Dictionary of the English Language, Fifth Edition. (2011). Retrieved October 24 2015 from http://www.thefreedictionary.com/soundness.)

Wikipedia offers the term smoke test as synonymous with sanity check for software testing.

For the record, I think sanity check is more recognizable and an acceptable phrase.

I don't think "sanity check" is ableist, really, because it's using a different meaning of the word "sanity" (which is a positive term to begin with).

If I run a "sanity check" to make sure the internal state makes sense, I'm not saying that the program might have severe mental illness: I'm saying I want to make sure everything is internally consistent before proceeding further.

That's a separate meaning of "sanity": that everything fits together and nothing is obviously wrong. It was actually the more common meaning in the original Latin, with the idiom for "not having a severe mental illness" being instead compos mentis (literally "having control over one's own mind"). Saying that a person was sānus or had sānitās generally meant that they were in good physical health. Modern usage has shifted significantly, but this older meaning is still around to a lesser extent.

So I don't think that using "sanity" to mean "consistent and with nothing obviously wrong" with respect to a computer program is ableist language. To use an analogy, if I called someone with a disability an "invalid", that would be wrong. But saying that text input in a numeric field is "invalid" is a separate usage of the word, referring to an objective fact, and has been used for decades with no offense intended. In this case you're not even using the negative term "insane". And none of the lists of ableist terms I've found (e.g. here, here, and here) have included "sane" or "sanity".

In short: I don't think there's anything particularly wrong with the phrase "sanity check". It has a long history of technical use and I have never seen the phrase called offensive anywhere else. Consistency check might be the best alternative, or if you want to be pretentious and avoid English connotations Probātiō Sānitātis, but neither is ideal: the sort of "consistency check" run by fsck is a different sort of beast, and pretty much nobody is going to recognize the Latin.

When it comes down to it, language is meant to facilitate clear and meaningful communication. If new terminology gets in the way of that goal, it's not performing its proper function—so you might want to do a sanity check on the system before trying to institute a new phrase universally. ;)