I don't think this can be gamed as some sort of strategic choice. The Supreme Court overruled a very poor precedent (none other than Justice Ginsburg has commented on the sweeping overreach embodied in Roe v Wade) and returned the matter to the political arena, where it belongs. There are some very socially conservative states that will have strict anti-abortion laws. But that's not where most of the country is (including quite a few red states). The places where it will remain as an issue are those where referenda are not available as a tool for settling the matter. In those cases there could be a divergence between what the political system produces and what most of the voters want and it will remain a contentious issue. In most of the country it will get settled and we will move on.
It could also be that abortion will remain an issue in national politics long after it has been settled in most states. But I suspect the Republicans will eventually adopt a politically neutral federalist position on this. Abortion is bad but should be left as a matter for states to sort out. Ditto for the Democrats. What's interesting though is that there is a strong faction in both parties that want it to be a federal issue. I don't think they will prevail but it is not out of the realm of possibility that it will remain a potent national issue after most states have settled the matter.
Having a person run for national office that is championed a strict abortion law (the right choice) is a loser in toss-ups and rust belt. Those that can't see that are fools.