I'd much rather it be a thing that just starts to happen, without any Infinity Stone hijinks involved. Part of the appeal is in not knowing - that creepy, it-could-happen-to-anyone feeling that maybe your family contains the X-gene and now your kids are freaks. Tying it into the gauntlet just seems lazy.
I saw someone say that they could explain away the prior existence of the original X-Men (maybe a small team, plus Xavier) by having Xavier mind-wipe anyone who they ever came into contact with during their heroics, but the mutants are starting to pop up so rapidly that they're forced to step into the spotlight now.
Besides, having mutations start with the Infinity Gauntlet removes any possibility of pre-2019 stories involving Logan, Xavier, Magneto, Apocalypse, Sinister, Omega Red, etc. etc. Or rather, means you'd have to bend over backwards to tell those stories around a hasty decision to get mutants into the universe ASAP.
Disclaimer: I gave up on that guy's theory after about 2 paragraphs.