And questions of mutant powers aside, it's worth noting that the X-Men have fought a great many non-mutant villains as well such as Tyrranus, the Cobalt Man, Count Nefaria, Locust, the Stranger, Man-Ape, Lucifer, Porcupine, Eel, Plantman, Scarecrow, Unicorn, the Maggia, Kukulcan, the Z'Nox, and the Super-Adaptoid amongst others. Fighting non-mutants is not in keeping with the first dozen or so X-Men appearances, but it does tally with the rest of the run.

Regarding telepaths, aside from the tiny handful allowed by Eric, the X-Men have ties to the White Queen, Cable, X-Man, Rachel Summers, Quentin Quire, the Stepford Cuckoos, the Phoenix Entity, Xorn, Legion, and others. So, yeah, telepathy's a thing in the MU, especially the X-Men's wide-ranging corner of it.

I know the X-Men, on at least two occasions I am very familiar with, have had to deal with time anomalies. 

Kang isn't a mutant, but would the X-Men's experiences of time travel assist them in any way (referring to all incarnations of the X-Men, I don't recall the original team dealing with time anomalies in the 60s)?

I'd always wanted to see a Hulk/Kang encounter, but I suspect brute strength would only last so long against Kang the Conqueror!

So they want to try the "shooting your own grandfather" storyline? And from a supposedly smart character like Hank McCoy? If the X-Men change the past, either they will eliminate their own timeline, or (as per Marvel chronophysics), create an alternate "What If" timeline.

It almost made sense in "Days of Future Past" when their present was so terrible that any time changing risk was acceptable. Then the writers continued to mine the future with characters who came back, seemingly unaware that changing the present means changing the future.

I guess an integral part of Robbie's initial question, Kang vs. X-Men, depends on who wrote it.  There are a bare handful of writers who could handle such a plot with enough discretion to make it work... and fewer every day, it seems.

Agreed.

It's best not to overdo any idea. I really enjoyed what our host did when he had Superman and Phantom Stranger team up in a late 80s ACTION COMICS issue. It was something different. But if Superman were to start having supernatural encounters in every issue, I might tire of the concept.