The curiously-named repopulation paradox is not a paradox
at all, just an instance of confused thinking.
In context, it concerns the question of whether people in the future (i.e. not alive at the present time) can have rights which we can or should respect. For example, a right to clean air. If we do decide to accord such rights, then it follows that we should take all necessary steps to ensure that they are respected. Hence, rights-based ethics.
The supposed paradox is that the existence of such people directly depends on our actions at present. We cannot imagine a specific person alive 100 years from now who, under one particular policy, does not have clean air, then alter the current policy such that he does, since almost certainly as the result of the alteration in policy the world would no longer contain this specific person. In the fanciful jargon of the paradox-maker, the world has been "re-populated" by the change of policy.
Now, supposedly, rights can only be granted to specific people (or other entities). That is, it is logically impossible to give X a right to clean air (say) if we don't know who X is. However, since it is clearly impossible to specify individuals 100 years in the future, we cannot consider them as having any rights at all.
Note that this is logically distinct from granting future rights per se: no objection (except possibly sexism) is raised to granting the eldest son of Y the right to enjoy his inheritance when of age, even though such a person may or may not exist: because if such a person does exist he is already unambiguously specified (up to paternity suits...).
This example gives us a clue as to why the supposed paradox is not. If we are fair-minded, for the great majority of rights that we might wish to bestow, we wish to bestow equally on all persons alive at a given time and place. For example, one might wish to bestow on the people of Iraq the right to a free and fair trial, or freedom of speech. And this wish would obtain whether Iraq's population consisted of the people currently alive there, or another set of 23 million people with entirely different names, shoe sizes and tastes in music. We do not have to specify entities very much to give them rights. (We say "people of Iraq" simply because Iraq is a convenient geographical division of the world.)
Since we can, and do, conceive of giving rights to groups of people who are only very weakly specified, we can quite legitimately conceive of giving rights to people living 100 years in the future. Always assuming that there are people alive then. Like "people of Iraq", "people living 100 years in the future" are already specified enough for us to think of their rights.
The fallacy of the supposed paradox can be even more easily seen by considering the question of whether we want people in the U.S.A. 30 years from now to have the right of trial by jury. Decisions being made now (for example, which Supreme Court justices to appoint, which President to elect) may well affect this right in the future. Such decisions will equally have some effect on the future make-up of the population. But we don't conclude that it is therefore impossible to consider people having this right in the future.
One of the great abilities of human intelligence is generalization: the ability to conceive of classes of entities, and not just individuals. We have used this ability to imagine giving rights to people in general, who would receive such rights merely by virtue of being human. We might discuss giving rights to individuals by virtue of their being specific people and not anyone else, for example whether John Kettley, or Annabelle Giles, should have the right to clean air. But such a discussion is by its very nature inequitable, if not iniquitous. For any right worth the giving, we would give it equally to one set of people or to their "re-populated" replacements: to the people living 100 years from now, whoever they may be.
Of course, it may be that in a few thousand years humans have evolved to benefit from particulates in the air; or are living mainly as disembodied brains. But that's a simple problem of our inevitable ignorance of the far future, and no paradox.