the only thing we have now that i think would impact birth rates in a high-tech socialist future is low infant mortality.

pretty much everything else that pressures people to have kids or not have kids is rooted in patriarchal religion and the capitalist hellscape. Who knows what people would do without losing career prospects to raise children, without god telling them to be fruitful and multiply, without despairing climate change, and without the imposition of the nuclear family? hell maybe the population would even go up more.