It may have been a joke, but people are idiots. Many think that overturning Roe would mean the criminalization if abortion throughout the country (a myth the media and abortion rights activists pretty much never correct), so plenty of low-information, radical feminists who have never read Roe would lose their minds if it got overturned. I could see them calling for secession like some in California are.
Frankly, I think it would be somewhat anticlimactic. Sure, you'd see some red states ban it, and the media would make a big deal out of it. However, when the ignorant people eventually realize that the world didn't come to an end and that you can still have an abortion in many states, the **** storm of idiocy will die down. They might even eventually realize that they were actually the ones forcing their views on people, not the other way around, but I won't hold my breath on that.