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
Are you saying that even without time travel, free will is an illusion? Surely there has to be a time travel scenario, like going back 1 second in time and shaking hands, where all information is known to both travelers, and the future self would know what was done previously, and can choose to take a different action.