Sure, now ask them "should elective abortion be legal?" And then you'll immediately see the conflict between the two positions. The fact that they may both support contraception is whataboutism. The core objectives of the two groups, are indeed directly contradictory.

You missed the point, which is that there is a difference between the substance of an issue and the combative political campaigns set up around an issue.

The substance is not binary; there is substantial overlap and gray areas. Most things are not zero-sum. But it’s beneficial politically to set up an “us vs them” mentality.

So yes, you’re right that the people are in conflict. But the point is, much of that is artificial.

The substances may overlap in some areas, but the defining goal of two groups are often directly contradictory. The goal of a group whose primary goal is to criminalize abortion is directly contradictory to a group that wants to make or keep abortion legal. The fact that they may both support contraceptives is missing the forest for the trees, the primary goals of the two groups are indeed directly contradictory. Achieving the goal of one necessarily means the other fails in their goal. There's nothing artificial about this.

You are correct that those two movements are not completely contradictory. First, it must not be assumed that everyone who is pro-choice will always chose abortion. Second, neither the pro-choice nor anti-abortion movements seem to have a large scale plan for the care of children born from unwanted pregnancies. So there are areas that are not contradictory.