1981, by my reckoning, was the year in which Marvel's mutant population became the subject of a franchise. I'll admit up-front that this is very much arguable. One could choose 1975 instead - that was the year that saw both Uncanny X-Men return and The Champions debut, both of which included mutants in their line-up, as well as seeing Beast join the Avengers (which had already featured Scarlet Witch and Quicksilver in their ranks).
To my mind, though, it wasn't enough for mutants to simply feature as main characters. I don't think the X-Men truly became a franchise until multiple books were available about being a mutant. The Champions and The Avengers were both "standard" superhero team books (I mean to imply no criticism in that phrase). Dazzler, by contrast was, like UXM, about - at least in part - the difficulty faced by being part of the mutant race. That, to me, is when mutants stopped being the concern of just one book.
There's probably also others that might want to go for 1982 instead, since that's when Marvel Graphic Novel #4 introduced the New Mutants, and also when the first limited X-Men series, Wolverine, was published. I guess it comes down to whether you see Dazzler as part of the X-books series (since it's about a mutant who originally appeared in UXM and who struggles with her genetic status) or not (because it's about a singer who has no interest in getting involved with the struggle for either mutant rights or the punching of evil in the face).
All that said, then, what did 1981 bring us? Well, as mentioned, we got Dazzler, which grew from a rather underdeveloped and throwaway special guest-athon into something perhaps ahead of it's time - a book in which superheroism isn't just seen as an interruption to everyday life (Spiderman had that covered) but an imposition to the point where the heroine actively tried to avoid any contact with the abnormal. That angle, combined with the significant sub-plots involving Dazzler's career progression and love life, ultimately caused sales to drop, which is a shame, and I wonder if that led to the book attempted to return to its original roots. Galactus sending Dazzler into a black hole is after all pretty similar to Doom sending her into the realm of nightmares, but in the later story there's no fretting over getting gigs under the belt to at least bring some spin to the rather by-the-numbers storyline. Even without completely dropping the slice-of-life stuff, I don't see how the book could become anything other than ludicrously schizophrenic. I guess I'll see when I finish the first Essential volume.
Over on the book that started it all, meanwhile, Claremont was now into the seventh year of his run, and by this point he had most certainly got his eye in. Some of the most famous X-Men stories had already been and gone - the initial Shi'ar/D'Ken storyline, the "Dark Phoenix Saga", but 1981 saw the first full year of Shadowcat in the team line-up (I may not have liked the character back then, but I can hardly claim she wasn't important), along with the now-classic "Days of Future Past" story. If a story's impact can be measured by how many times future writers return to it (at least in name), then this must surely be in at least the top five X-Men stories ever written.
This was also the year that provided some long-overdue complexity to Magneto, the X-Men's oldest foe. UXM #150 re-cast the man as a principled man so deluded by his experiences that he'd somehow become a callous terrorist. This new approach to Magneto would be template for later years, and lead to him regularly featuring in the top echelons of "greatest comic villain ever", and with good reason.
All this, and the Brood too! I'm not sure I'd go so far as to say 1981 was a pivotal year for the comic, so much as part of a pivotal era that lasted for a great deal (though by no means all) of Claremont's run. Having said that, we're clearly at the start of something, and by the end of the following year, there can be no doubt that we'd reached the point at which the X-franchise was up and running.