[ukj]

For me (intuitively, conceptually and abstractly), the AC is just a particular case of Hilbert's Entscheidungsproblem.

It doesn't matter what the AC states. All that matters is that you interpret it as a proposition. And then it's sufficient to assume that some algorithm can be constructed, or some Oracle can be consulted to determine the truth-value of the proposition.

Like, for example. I can construct you an Oracle which evaluates the "Law" of Non-Contradiction as true.

https://repl.it/repls/GiftedHumiliatingProcess

This is the fundamental (only?) difference between mathematics and programming. Mathematics assumes pure functions.