What people forget in the abortion debate is that contrary to the popular impression there aren't 2 sides to it. There are 3 factions in it, at very least.
1. People who want abortion heavily restricted, preferably from the point of conception, with their view based on deeply held religious beliefs usually. Usually willing to carve out exception towards situation where the pregnancy may kill the mother, but not much beyond that.
2. People who want abortion anywhere, anytime, for any reason, or even no reason at all, at taxpayer's expense preferably, no questions asked, due to a different kind of deeply held belief. Usually highly idealist progressives, leftists, feminists. They see this issue as a black and white one too - abortion being a right, a long awaited liberation from one of many raw deals nature gave one of the oppressed groups, which, as such, should be made as easily available as remotely possible.
Both of these sides make the bulk of activists of their respective sides, and it is extremely rare for them to change their view on the issue, as it would have to come with a change of their whole worldview to make sense. Likewise, they are not commonly getting people who have developed other views to come to their side. As the descriptions imply, both see the current setup as a dirty compromise, but still more acceptable than the other side winning completely. However, what they can do is make appeals to all the voters who don't qualify into either of these groups.
3. The weirdos, moderates, uninvolved, wannabe medical ethicians and so on. People who for whatever reason consider the abortion issue a question of underlying medical facts, philosophical assumptions, and competing rights of unborn child and its mother, social policy, or any combination thereof, who, as such are willing to adjust their opinion on account of argumentation about such things.
What conclusion shows up here most clearly is that any arguments that are supposed to change anyone's mind about the issue, nevermind change their vote on the basis of such (for obvious reasons groups 1 and 2 care about it more than 3, which, having more mixed feelings on it, is less likely to consider it a make or break issue for their voting preference), will need to be aimed at group(s) 3, preferably to as wide of a section of these as possible.
For one, as long as just knocking down the regulations down to state level goes, this is hardly the worst things as far as repelling moderates goes. Sure, it will seriously anger group 2, but lets be honest, they would never consider voting for GOP either way, not with today's ideological polarization.
For those who want more decentralization, also great news.
Those who live in blue states also won't be affected, unless they are highly political group 2 members who get angry at what red states do, or ironically, stand to benefit from abortion tourism to their state.
It is going to affect people in states that want to restrict abortion more than Roe allows. And who would that be? I'd guess that would mostly be the denizens of blue colonies cities within red states, and slightly discourage group 2 people from living there, which may have some dynamic interference with such events like the California exodus.
It will mobilize the religious conservatives, especially combined with inevitable promises by upcoming democrat candidates to do what they can to liberalize abortion again, while also, if such a thing is even possible after the height of BLM craze and constant transgender politics in the media, mobilizing the democrat base further too, for similar but opposite reasons.