Timelines were handled in arbitrary and disparate ways. This movie was just one more way to handle time travel. When Sisko looks at a picture of himself as Bell, there is more than a little bit of an inside joke. The Enterprise assisting Cochrane was also over-the-top.
These stories completely neglect the likelihood that even a minor change would disrupt the future enough that they would never exist at all, especially when one considers the infinitesimal possibility that a particular sperm would fertilize an egg.
I hope that Star Trek in whatever future form it may take will embrace the parallel universe approach and retcon the past stories to fit into this understanding of time travel.
Time travel in Trek more than most of the rest has been straight fantasy, but Star Trek has had pretensions of being science fiction. I'm happy that these new writers and production team honor the sci-fi side of Star Trek with a more plausible time travel mechanism.
Every Star Trek series has been a reboot or reimagining of the universe. This contrast is brought into hilarious relief in "Trials and Tribble-ations," especially in the scene in which Bashir is confounded: "Klingons, I don't see any Klingons."
Trek has always been able to laugh at itself, to poke fun at the fantasy.
This strategy of fitting the future in with the past is in the best tradition of Star Trek shows and movies that preceded it.
Often, to enjoy Star Trek, you just have to smile and laugh at the silliness beneath the surface. The augment-virus, ancient humanoid, warp-ten salamander, barclay-devolving-into-a-spider, hippie alien, toga alien side of Star Trek is part of the fun.
If anything, this new Star Trek takes itself more seriously than did the campy Star Trek before it.