Why do you think religious conservatives are so adamant about abortion or contraception?
I think you haven't understood the exact question. Opposition to abortion or contraception are policies; racial differences in intelligence are an entirely external fact which should only affect policy after you filter it through the lens of your ethics. A better analogy would be confronting a Catholic with a claim that allowing abortion would make for much less poverty and death in the 3rd world. And even then, a liberal confronted with race differences in intelligence would not be similarly pressured to allow e.g. apartheid, if there is an explicit and sufficiently high value for moral equality between the races in the liberal mindset, and this moral equality demands some sort of practical egalitarianism!
What I claim in this particular example is that, since the secularization of progressivism/liberalism around the Enlightenment - and its pragmatist/utilitarian posturing - it has been having trouble deriving moral equality from first principles here, and deep down there's awareness of that. So liberals desperately try to derive an egalitarian "ought" from an inconvenient "is" - even though nobody's forcing them to!
I think you haven't understood the exact question.
It wasn't exactly analogous, but it wasn't meant as such. If I wanted to do that I would have brought up Creationism among Protestant Americans.
I fundamentally think there are very strong sacredness based feelings around this that are not based on consequences in the real world any more than other kinds of religious thinking is. There obviously are good secular conservative arguments in favour of religious thinking guiding how our society develops though.
As Multiheaded added, "Personal is Political" stuff like gender relations, etc also may belong here.