The term that should most-thoroughly suit your need is
The term is very common in common usage, and means precisely what you're asking for (instead of, no offense to @SF, 'moot' which means an irrelevant, due to the past-tense implication of the word. A catch 22 has no implicit or explicit temporal locus.
This fits the question, because when "all of possible outcomes are ultimately equivalent despite being presented as different" the reason for the equivalency stems from "contradictory constraints or rules" (Catch 22) which, generally, were not initially seen because of the poor deductive powers of someone involved.
The situation in Heller's novel, Catch 22, is identical to the question:
any pilot requesting a psych evaluation, hoping to be found not sane enough to fly (and thereby escape dangerous missions) would thereby demonstrate his sanity
There are two choices (on the part of the doctor):
- the pilot is insane
- the pilot is sane
but actually #1 is the same as #2 in this context. The choice of sanity really isn't a choice. It's a Catch-22