They rail about how not being able to hurt certain people would infringe upon their rights. How it is an integral human right--for them anyway. How they would be suffering unfair discrimination at the hands of an oppressive government and people of other groups who are bigoted against them. Their oppression is obvious, even if they have not yet actually been banned from oppressing; they do not, and never will, see their victims as people.
And then the anti-gays see this and smile and nod, and call the pro-abortion people hypocrites and point out how ridiculous and awful they are. And vice versa.
Because they are on opposing sides of a false "conservative" and "liberal" dichotomy, and not because they are any different from each other.