Quote: "One possibility is to treat AC as a powerful drug and take it only when necessary. Theorems should come with consumer labels saying what went into them. So if you see a box on the shelf of 'Banach and Tarski’s Miracle Duplicator! Feed Multitudes!', it will say on the back of the box 'Contains AC'."
Indeed, many mathematicians are sensitive to this and try to point out when they invoke the Axiom of Choice, and there are other mathematicians who deliberately seek non-AC-powered variants of theorems in order to put them on less nebulous and more constructive ground.
Personally, I view AC as another reason to consider more generalized foundations of mathematics. For example, if you know anything about topoi, it turns out that we can view set theory as a topos on a point, and any topos on a complete Boolean algebra comes pre-equipped with an inherent axiom of choice! [0]