There are non-political ways to address this, such as better contraceptives like Vasalgel.
EA already has semi-official positions on intractable political issues like immigration. If stable two-parent families are indeed an effective way to prevent child abuse, I don’t see why we shouldn’t have a semi-official position on promoting those as well. It could help address conservative underrepresentation in the EA movement. I think if some positions are taken publicly on both sides, that increases our credibility as an independent source of truth. Otherwise we might be seen as “EA-washing” the political positions that we already held as coastal liberal types.
But really I think stable two-parent families are a bipartisan issue. For example, abortion probably helps reduce the incidence of single motherhood (though of course the ethics of abortion itself is another can of worms). I don’t think your average liberal person is actually against fatherhood or stable households, they just prioritize other outcome measures (perhaps incorrectly if the data here is right).
In this sense I think the govt should create appropriate incentives for long term committed relationships where children are concerned—perhaps like a no claims bonus (an increasing yearly benefit of not crashing a car in the UK) for each year parents with children who stay together until their last child is 18?