The Continuum Hypothesis and the Axiom of Choice

The axiom of choice and the continuum hypothesis have kind of a curious relationship because they, okay, the continuum hypothesis from a set theorist pointed you to construct a lot of exotic things. So for the rest of us in math outside of set theory, should we be losing any sleep over the, what seems to be kind of indeterminate status at the moment of the continuum hypothesis? We're told it's undecidable in the standard model of set theory. You know, does it matter? Does it affect the rest of math? The answer mostly is no, but it's not entirely no.