Some ideas are:
- You branch off into another timeline and your actions make no difference to the previous timeline
- You’ve already taken said actions but just didn’t know about it so nothing changes
- Actions taken can have an effect (so you could suddenly erase yourself if you killed your parents)
- Only “nexus” or fixed events really matter, the timeline will sort itself out for minor changes
- something else entirely
Logically speaking it’s the only way time travel can be done, and for bonus points physics wouldn’t have a problem with it.
Any Back to the Future shenanigans is just creating alternate realities, which may or may not instantly destroy the original.