It's more complicated, in the case of telepathy, 'cause it can also be *learned* by non-mutants who go through magical training, like Dr. Strange, Dr. Druid, Baron Mordo, Enchantress, etc. (it was one of the 'trained' abilities back in the Marvel Handbook days), and be taught by aliens, as in the case of Mantis, Moondragon and the Uranian Bob, from Agents of Atlas.
And there was the weird bit where Jean was a telekinetic, until Professor Xavier somehow taught her telepathy (as well as giving Changeling telepathy so that he could impersonate Xavier temporarily while he secretly faced off aliens or whatever), although that first bit has been retconned into her always having been telepathic. (But Xavier 'teaching' Changeling telepathy remains canon, AFAIK.)
The non-mutant Kwannon somehow learning telepathy as a side-effect of being possessed by the telepathic Betsy is another odd example, and suggests that Storm or Iceman could someday develop telepathy because they have been possessed by Emma in the past!
In short, goodness. It's a mess. Kind of a relief that Colossus can't just sort of 'teach' people (even non-mutants!) to armor up, or Kitty can't 'teach' people to walk through walls!