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
Only 1 timeline matters. You’re own. Everything else becomes fluid around your timeline when you time travel.
The timeline IS fragile, but the whole of existence is not in regards to time travel. If you go into the past and change it, the timeline changes, but only because the original timeline had you going back and changing it. You can see yourself. You can interact with yourself, but if everything is exactly as it should be you really don’t want to go mucking around and find yourself in a world where the south lost the civil war but things are thousands of times worse and you killed the ancesotor of the inventor of time travel after breaking your machine and can no longer access the timeline to fix any issues you may have caused.