Even if certain states passed rigidly anti-abortion laws, state borders are porous; back in the 1980s, in my native state of Idaho, the drinking age was 18, while the drinking age in neighboring Washington state was 21. The lines of traffic that Washington State University students created while traveling to bars in Idaho on a Friday night are still legendary. In the same way, socially conservative Idaho could outlaw abortion today, but the laws of supply and demand dictate that abortion clinics would begin to populate the Washington-Idaho border.
It should also be noted that—in spite of the claims of many federalists—governments at the state and local level are often not much more “pro-family” or “pro-life” than governments at the federal level. I know of no social policy that has proved more incipient to social degradation than no-fault divorce, condemning millions of children to grow up in single-parent homes and live lives of poverty. But this policy was—and always has been—administered at the state level. Nor are state and local laws always representative of the communities whom they regulate. It makes sense that no-fault divorce would begin in California, but seems anachronistic that the last state to resist it would be New York, which did not liberalize its divorce laws until 2010.