It is not clear that we really can make sense of the idea of someone who is otherwise rational but cannot see how facts about his future can, by themselves, constitute reasons for him to act in various ways. (McDowell, 'Are Moral Requirements Hypothetical Imperatives?' in M. Smith (ed.) Meta-ethics, p.107.)
But, as Parfit points out in Reasons and Persons (p.140), there's a strong analogy between 'I' (vs others) and 'now' (vs future). The aprudentialist might argue, "I don't care about my future self - I only care about me now. So why should I take my future self's interests into account?" It seems likely that whatever answer we give will apply, mutatis mutandis, to the amoralist too.
To bring out the analogy, notice that our aim in practical reasoning is always to answer the question, "how should I now act?" -- it is relative to a time just as much as it is relative to an agent. Now, we are tempted to say that the "agent-now" (i.e. present time-slice of the agent) is being irrational in neglecting his future interests, because his future self will suffer as a result. But neglecting other people's interests will likewise expose them to extra suffering. If an agent-now can rationally ignore the suffering of others, parity of reasoning would seem to suggest that he may likewise ignore the suffering of his future time-slices. (Of course, most of us are, as it happens, concerned about our future selves. But then, most of us are at least mildly altruistic too. That doesn't show we must be, or that anyone who fails to share our perhaps idiosyncratic concerns in these respects must necessarily be irrational.)
We might defend prudence by arguing that reasons are 'timeless', so if X will be a reason for you in future, then that very same consideration must be a reason for you now. But if reasons are neutral between time-slices of people, then why are they not likewise neutral between people? This reasoning leads us to rational altruism: if X is a reason for you, then it's also a reason for me.
So the problem, you will notice, is that rational egoism is "incompletely relative". It allows time-neutral reasons, but not agent-neutral ones. Such inconsistency is troubling. We would do better to accept both or neither. If we insist that it is irrational to discount one's future interests, then we should likewise conclude that it is irrational to discount the interests of other people. But we are not forced into rational altruism. We might instead accept that even the aprudentialist need not be irrational.
A (very unusual) person might ignore their future interests without thereby making any logical or empirical mistake. If they genuinely do not care about their future interests, then it is not clear what grounds we have for calling them "irrational". Most of us are committed to the prudential point of view. But it isn't clear what non-question-begging, non-prudential reasons can be given for adopting this view. So, on reflection, we see that it is just as rationally legitimate to work within the framework of present-concerns instead. As with the rival viewpoints of self-interest and morality, these frameworks are simply incommensurable. There are no independent grounds for favouring one over another. Each person (or time-slice of a person!) must simply choose what sorts of considerations they will recognize as reasons, thereby deciding what sort of person they want to be.
Update: I should add that the analogy become especially forceful when coupled with Parfit's reductionist view about personal identity, according to which the persisting ego is an illusion, and there is no further fact beyond the various physical and psychological connections and continuities between time-slices.