Readers will expect cultures to behave in what seem to them "logical" fashions, despite the evidence of the real world that they do not.
Therefor, when producing a society in which there is both a serious need to keep the population down, combined with a widespread general oppression of women and/or homosexuals, please to point out to the reader some of the underpinnings of those attitudes.
Also, Bear, it is important to note that a significant proportion of readers are not going to pick up on the fact that if you wipe out everybody in the Northern Hemisphere, your remaining population is likely to be heavily skewed Muslim and Catholic.
However, comma, if one more person says to me "But if you are trying to limit population growth, you're going to be encouraging homosexual relationships," I'm going to bite them on the unfounded assumption.
Because, first of all, being gay doesn't mean you don't want to have kids, and in a society with a better-than-21st-century level of reproductive tech, it doesn't mean a damned thing anyway (we have birth control and we know how to use it.)
Let's talk about institutional homophobia in 20th century China, for an example.
Bias is not founded in logic. It's founded in the fear of people who are Not Like Us.
On the other hand, enough readers are ripping on that particular issue that I guess I need to 'splain.
...no, wait. No time. I sum up.