Overpopulation is the opposite of our problem. Uncontrolled immigration is the only thing masking a demographic collapse in the US. Fertility rates are at historic lows, far below replacement levels.
It is the same problem in Western Europe, Russia, and Japan.
Yes indeed, but the Sierra Club had an opportunity to voice their opinion about immigration and after due consideration for the politics, they decided the US should be neutral about immigration because the immigrants voted for their party.
What actually happens is that when the standard of living is raised and families can count on children reaching maturity, they reduce their birthrate below replacement. This can happen in the third world if they achieved a higher standard of living.
Note that some religions may not follow this rule, but in general there is a stable human population out there somewhere.
The trick is to get there and see if the climate really is unstable (which I doubt).