If anything is going to generate a "civil war" in the near future, I would think it is the Jan. 6 investigation and if Trump runs for office again. If you ignore the political bias and just look at the evidence being shared, it is pretty damning. He literally tried to become an autocrat. People will stand up for democracy. If Trump gets punished, right wing asshats will go "peacefully protest". And if he gets away with it and gets reelected, left wing asshats will "cry" and "riot". I personally think the extreme right nuts are more likely to cause a divide.
Otherwise, the majority of Americans didn't want Roe overturned. I personally don't care about abortion rights. I do care that the SCOTUS seems completely tone-deaf. They were more upset about the doc being leaked than whether or not they were making a decision for the majority of people. The power trip over idealogy is the problem. Given Roe, the religious school decision, and gun rights as well as the other rumored cases they are looking at, I think SCOTUS is going to cause a national issue if it goes unchecked by the forever gridlocked senators. But I don't think Roe is the trigger for a "civil war". Left wing people protesting are too passive to do something about it.
Ironically, overturning Roe, SCOTUS just said that privacy is not constitutionally protected. Given the internet privacy legislation by Republicans to punish tech companies, they might have just shot themselves in the foot.