This post isn't really about time travel. It simply uses time travel as a theological illustration. An analogy for prophecy and prayer.
i) Time travel is a popular scifi convention. Indeed, time travel accounts for some of scifi's popularity.
ii) There are variations on time travel. Traveling into the future or into the past.
There's also the question of changing the past. The familiar scenario of a time-traveler who goes back in time, and either intentionally or inadvertently changes the past–which, in turn–changes the future.
That can generate antinomies, like the grandfather paradox.
One question is whether it's possible to make discrete, self-contained changes to the future. If so, retrocausation might not be incoherent in those cases. If, however, even one change has a ripple effect, then his action destroys the future he came from–which is incoherent.
iii) However, the principle can operate in reverse. Suppose a man travels into the future. He may do so out of sheer curiosity. Or he may do so to escape the present.
Suppose he's appalled by what he discovers. In-between, there was a global catastrophe. He therefore returns to the present, forearmed with his knowledge of the future, and attempts to avert the dire outcome.
This isn't prima facie incoherent in the same way that retrocausation is. He didn't originate in the future he changes. And present events cause the future. So his action doesn't necessarily disrupt the linear direction of cause and effect.
Of course, on this scenario, we're dealing with two different futures. The future which will eventuate if he doesn't act on his foreknowledge, and an alternate future which will eventuate if he does. The alternate timeline that replaces the future he initially visited is subsequent to the former. So that's still consistent with the linearity of time and causality.
It's possible that this is subtly incoherent, but, if so, that has to be teased out.
iv) There is, however, another possibility. A more fatalistic scenario (on one definition of fatalism). Perhaps he doesn't change the future he visited the first time around. Perhaps his efforts to change the future unwittingly contribute to the very outcome he was endeavoring to avoid.
He knows something about the present, and something about the future (that he encountered). But he didn't witness the intervening events. He doesn't know the chain of events linking the present to the future. Hence, his efforts to change the catastrophic future might be a necessary condition for that to happen. Due to his ignorance of the intervening events, he ends up precipitating the very disaster he was laboring to preempt or prevent.
v) Apropos (iv), some freewill theists consider predestined prayer to be otiose. If the future is etched in stone, then nothing we say or do in the present can change the future.
However, prayer could be like the time traveler in (iv). What he does in the present has results. He contributes to the future he prays for, not by changing the future, but by acting at present in ways that, unforeseen to him, fascinate the outcome he prayed for. Prayer needn't change the future to be instrumental in realizing the future object of prayer.
vi) Some time travel scenarios focus on a different dilemma. The traveler has seen the future. He's aghast. He returns to the present to warn his contemporaries. He desperately exhorts them to take necessary countermeasures, before it's too late, to avert disaster.
But he confronts a conundrum: how does he convince anyone that he knows what he's talking about? Although he has seen the future, they have not, and they have no reason to believe him. Indeed, they think he's a raving mad man.
Out of frustration, he takes matters into his own hands. He attempts to sabotage the source of the impending catastrophe.
As a result, the authorities view him as a crazed domestic terrorist, and lock him up in a secure facility. Indeed, he might have been involuntarily committed just for crazy talk, but his subversive activities seal the deal.
In theory, this, too, could precipitate the catastrophe. Due to his actions, they tighten security measures, thereby ensuring the disastrous outcome.
Confined to his padded cell, his prevision becomes a curse. He can't make anyone take him seriously. The harder he tries, the worse it gets.
Depending on the story, the character may know enough about the near future to make a few short-term predictions that indicate he really does have advance knowledge. That may persuade a key person.
However, that may confirm the suspicion of authorities that he's a domestic terrorist who's privy to terrorist plots. He only succeed in persuading them that he's dangerous!
This is much like the situation of OT prophets. Having previewed the future, they warn their contemporaries to repent before it's too late avoid judgment. But like the hapless time traveler, his contemporaries dismiss him as a crackpot. A cranky lunatic. They find out the hard way that he was right all along.