Not at all. It's very easy to imagine it going the other way. Midcentury liberals were all about extending human rights to new groups of people and I could reasonably see Republicans defending Roe for economic policy reasons in an only slightly different work.
Possibly, but remember during the 1972 presidential election McGovern was tagged as the candidate the supposedly favored "acid, amnesty, and abortion." I guess this is a sign that the Democrats were friendlier to abortion rights than the GOP even before Roe was decided.
It would have depended heavily on the state and type of candidate. The Kennedys were famously quite pro-life until they stepped into line.
You could imagine a mildly pro-life Southern Dem getting the nomination in 1992 when they were desperate after 3 terms out office and willing to make whatever deals they needed to get back in. They went with an economic moderate IRL, but no reason it couldn't have gone the other way.
Yeah, I think the closest we could imagine to a "flip" is simply having both parties divided. The GOP has had a "Puritanical" streak in it since the beginning that it inherited from the Federalists, and I think there was always going to be a fiercely pro-life component once the issue gained prominence. So for me, how much either party favored one side or the other in their official platforms was always going to come down to how strong/organized the following groups were:
1. The "Puritanical" pro-life movement among conservatives in the GOP.
2. The "pro-life-by-coincidence" socially moderate Democrats like Southern Yellow Dogs and Northern Catholics.
Not only did #2 prove to be far weaker in our timeline, but the GOP successfully courted many of them, cementing themselves as even more pro-life. Another component is how much the pro-choice components of either party really cared about it. The more secular, feminist pro-choice component of the Democrats very clearly would never have been as compromising on the issue as tacitly pro-choice (but really more indifferent than anything) Country Club Republicans.