Disclaimer: This post is really about the philosophy of information from the future, not about prophecy strictly speaking, since prophecy generally has religious connotations. However, it made for a better title.
How we deal with information from the future depends, at least in part, on how we conceive of the progression of time itself. Basically there are two possibilities: one is a deterministic universe, in which events unfold, by necessity, in only one possible way, and the other is an indeterministic universe (surprise surprise), which for this discussion means either a universe in which events are controlled by probabilistic laws, genuine free will exists, or where all possible futures exist and are equally real. Obviously if you can get 100% reliable information about the future by any means you must live in a deterministic universe. (Side note: this means that if god exists and knows everything that will happen then the universe is deterministic. Now this doesn’t mean we lack free will of any kind, many people think that free will is compatible with determinism, for example Leibniz, but it does rule out the kind of free will in which the choice could really have gone either way.)
If the universe is deterministic and you have a 100% accurate method of getting information about the future then there are certain constraints about what information may be received. Specifically the information must be stable, meaning that the information received may not prevent that future from coming about. For example, if you resolved to do the opposite of whatever the information said you would do then you would not be able to receive the information about your future actions, unless events are in motion that will force you to change your mind or act against your will. Of course in a deterministic universe time travel isn’t necessary to have information about the future, you could simply take the physical laws and all the physical data and then compute what must necessarily happen in the future. However, this computation cannot take into account what will happen as a result of the computation itself (it must make its calculation based on all the facts except the ones describing the system performing the calculation), except possibly in cases where the predictions about the future contain stable information (this follows because of the impossibility of solving the halting problem).
In an indeterministic universe of course we can never have a 100% accurate method of determining information about the future. Even if we traveled back in time with the information events might still unfold differently than they did the first time. However, depending on the nature of the indeterminacy, certain information may still be impossible to receive. Specifically if the universe is one that unfolds based on statistical laws or genuine free will, but in which not every future is possible, then the information from the future cannot be such that it makes the future it is from impossible. Of course, in the case of the universe in which every possible future exists and is equally real this is not a problem.
But, in an indeterministic universe information from the future is much less helpful. Even if the information was the best possible, meaning that it comes from the most likely future, it is only reliable if it is about the near future. In even a moderately complex system possibilities tend to diverge over a short amount of time, and the smallest differences about they way events unfold (such as the way a butterfly flapping its wings) can have substantial long term effects. I don’t know exactly how fast the possibilities diverge in the real world (versus some idealized mathematical model), but I suspect that information about even a few years in the future would be extremely unreliable, enough to be worse than useless. (Of course the content of the information has some bearing on this as well, certain trends are less susceptible to divergence than others; information about what you will have for breakfast may be good only for a few days, but long term economic and political forecasts, which depend on many relatively stable factors, may be more reliable.)
Obviously pondering about information from the future doesn’t have any practical value by itself. As far as I know no one is getting any such information, or if they have been they aren’t sharing it with me. But, on the other hand, such considerations do have some bearing on the value of our predictions, which in turn has a bearing on our ethical considerations. A prediction is somewhat like information about the future, except much less reliable. But ideally when we predict we are learning something about what is likely to happen (if we are good at predicting), and so we could consider it information from the future in an indeterministic universe. And the fact that in an indeterministic universe information about the future is reliable only for short periods of time means that when we decide what to do we should weigh the short term consequences most heavily, and only pay attention to the longer term when a) it is extremely worrisome, or b) part of a trend that is unlikely to be changed (for example, if you kill someone they are likely to stay dead, although it is hard to say what other long term effects their death will have).