Whatever parts of the pro-choice movement that were influenced significantly by Sanger are almost certainly eugenic in nature. That said, I'm describing a course of action that I only certainly know occurred in the States.
Most liberals, I reckon, don't fully recognize this targeting of the black community. They're pro-choice because whether they regard the gestating life as a human being worthy of dignity or not, they consider its life less important than the concept of "bodily autonomy". They don't explicitly want dead black babies, but they aren't paying attention to the history of Planned Parenthood (which either does still want dead black babies/black population control or is just stuck in that pattern that leads them to establish themselves more in urban areas) and the disproportionate number of abortions among blacks wouldn't matter to them anyways because fetuses aren't human beings to them to begin with.
From a general political angle, the relevant part (and I can't say that they're intentionally working to screw over black people on this front) isn't "killing black babies" as much as it is "controlling the black population", which works in tandem with other societal forces (such as the destruction of their family structure) to destabilize and ultimately stagnate the black community.