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
My personal favorite?
Space and time is an infinite number of parallel realities that constantly compress and unravel at every possible random chance. We are 4th (or 3.5th) dimensional beings that experience the most probable result aggregated from an infinite existence. If you time travel back in time, and change the past, it would not affect the your past, but it would affect your future, if you time traveled back to your current time.