The major customers of abortion in the 19th century were middle- and upper-class native-born white women; and eugenicists raised the concern that these desirable classes would commit "race suicide" and be outbred by undesirable immigrants and poor people.

Conversely they were in favor of abortion and sterilization (frequently forced) for the poor and undesirable.

Did you know that when Republicans banned partial-birth abortion in 2003, they limited the penalty to a maximum of two years? Two years, for what pro-lifers consider murder?

Of course, the pro-choice side has its hypocrisies too. But they at least have can claim the moral high ground by being slightly more protective of bodily autonomy, and much more protective of the disadvantaged.

whereas a sufficiently powerful autocrat doesn't have to give a fuck what people say or think).

The sufficiently powerful autocrat doesn't have to give a fuck what people say or think if and only if his/her utility function is composed only of "staying in power". But people are more complicated than that and they tend to like to have other people share their views. Even most contrarians (who can be said to delight in having unorthodox views) try to convince other people of their views.

In the real world, the more powerful the autocrat, the more absolute the dictatorship, the more they care about what people say or think, the more restricted free speech is. I don't have any reason to believe that at some magical "sufficiently powerful" point, that direction gets reversed.

Conservatives for free love!

After all, that's what our honoured ancestors of the 1960s golden age were for.

It's not clear to me what you mean by "counterfactual" and "prima facie plausible" for these.

When you talk about real historical coalitions (like, say, anti-slavery evangelicals), in what way is that a "counterfactual" rather than, say, a "factual"?

Likewise, the one that you put on the list twice (pro-homosexual nationalists and anti-family nationalists) strikes me as prima facie implausible (if you have to grow it in competition, rather than having it in isolation and hoping it's stable).

Some of the combinations do highlight real intellectual divides- "libertarians for conscription" calls to mind Hayek's potential acceptance of a conscription law so long as it didn't impede the ability of individuals to plan. (Mandatory two-year service would work, whereas lotteries might not.) This was seen as a major disagreement by natural rights libertarians, who view conscription as slavery (and thus objectionable). But there seems to be a lot more chaff here than wheat.

Anti-slavery evangelicals.

I'm not sure why this one seems included. Evangelical Protestants such as they existed in the 19th century were a major part of abolitionism. The only reason this doesn't completely work is that modern evangelicals as we understand them were different in many ways from the closest thing in the first half of the 19th century.

This does however seem like a potentially interesting idea overall. The animals-rights/pro-lfe example is particularly striking. Pro-life/pacifists might be another possibility.

One thing that is actually similar to this is how often people presume that coalitions in other countries line up in ways that match one's own. For example, one common misconception among Americans about Israeli politics is that the nationalist/Zionist sentiment is coming from the ultra-Orthodox(charedim), when in fact many of the charedim don't want a Jewish state at all and it is the moderate Orthodox who are strongly nationalist.

Libertarians for conscription.

I've actually met one... or someone who claimed to be one, anyway. I think what he said was: "It's in the Constitution; if the government wants you to go kill some people, then you've got to go kill some people."

Sort of:

Nationalists for homosexuality

http://www.huffingtonpost.com/johann-hari/the-strange-strange-story_b_136697.html

Nationalists for homosexuality