You bring out sex-bots, and there are a billion men who will choose that over a wife, especially if he can have a maid-bot clean and maintain the home.
Population will drop by more than half in a single generation.
The irony being that the religious who refuse that type of technology will still breed, and the future depends on who shows up.
End result - more religious future, more likely the Butlerian Jihad situation someone mentioned earlier, in order to preserve the population.
Or you get religious communities copying the Amish model, divorcing from modern incredibly sinful life. And they remain in existence because they still have two kids, in a world where many have none and lifestyle pressure is only one.
Polygamy with a stay at home spouse still leads to reduced population, because a stay at home parent with four spouses isn’t likely to raise five kids to replace all the adults but raise two or so.
The synths like reduced population. They don’t have to use force to bring us to the optimum level.
I need to do more on the future of religion. You make interesting points.