Aside from the obvious
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Since states can still allow abortions, this means that a lot liberals will fuck off right back to their blue states (God-willing).
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It's not enough for states to ban abortions, though; they must criminalize it, because people are already talking about driving over state lines, getting an abortion, and then coming right back. Criminalizing it means that the person will be wanted in that state, and at the very least, cannot return. This should help make it that liberals MOVE out of red states altogether.
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Men and women will be more conscious about having unprotected sex. Hopefully, they'll look for serious relationships that will lead to marriage (won't hold my breath, though). Overall, it should lead to less degeneracy.
I don't think the actual number of abortions will change all that much. Many red states were already doing a lot to curb it so there isn't as much room to escalate their efforts as people think.
The biggest impacts are going to be the increase in state-to-state animosity and polarization and the potential for corporate influence to go mask off. Expect NGOs to spring up out of blue states that try to provide funding, transportation, etc. to red state women. Red states may respond by criminalizing such organizations out right.
Corporations are kind of a wild card. I tend to expect them to pick sides on these things, but they seem like they are pulling back a bit as of late. I think Republicans' willingness to clash with Disney has them a bit spooked, maybe. However, I don't hold the Republican party in high regard. Look how they are fagging out over gun control right now so they could start folding after the 2022 or 2024 elections. Will corporations try to pressure states into legalizing abortion? If so, how open would they be? If they brazenly challenge the will of red state voters, things could get very interesting. It would be a major disambiguation of the nature of power, the state, and what's going on in the world today.
One last thing to highlight is the parallel with Russia/Ukraine. The Russia/Ukraine war has put de-globalization pressure on the world and moved toward multi-polarization. The polarization between US states can, likewise, lead to a de-federalization. The subtext in both cases is the endurance of nationalism.