There's been quite a bit of discussion on the various forum threads on this over the past few months since all the various other car companies have decided to join the NACS bandwagon.
Biggest concern: Overcrowded superchargers.
Main reason this won't be a problem: The number of Other BEVs are minuscule compared to the huge number of Teslas out there; and Tesla hasn't stopped building out large numbers of Superchargers. As a result.. one can see the occasional non-Tesla BEV at an SC, but they sure aren't common.
At this point in time I believe that Ford is sending out free adapters; the other car companies (GM, notably) are planning to sell theirs. And I've actually found a couple of SC's around NJ that have the Magic Dock approach (i.e., both CCS1 and NACS on the same cable, pretty much).
Biggest problem I think I've heard is that most of the Fords out there have the charge port on the driver's side near the front. Tesla has suggestions on how to handle this in the short term (i.e., stacking all the Fords together in adjacent lanes, followed by an empty lane, followed by Teslas). In the long term, Tesla has requested that all the NACS-wannabees put their charge ports either on the front right (for nose-in charging) or the left rear, for backing in.
Just finished off a ~3000 mile trip to Texas and back for the eclipse and stopped at 12+ SC's on the way; none of them had a non-Tesla present.