Well, you would presumably still have the Starship Enterprise exploring brave new worlds, and probably a Vulcan or Klingon or two. You can still have something recognizably Star Trek even if you tinker with the details. Heck, apparently you can even skip the Enterprise part and set the series on space station called DS9 and still feel like Star Trek.
I mean, James Bond and Sherlock Holmes and Tarzan and Batman can survive multiple incarnations, updates, reboots, and continuities, but nobody ever confuses Mission: Impossible with The Prisoner. As long as the fundamentals remain intact, every different version of Zorro doesn't need to have the same continuity.
Heck, the new version of Galactica took place in a completely different universe from the old version. Didn't hurt it one bit.
That's just how remakes work.