There may actually be a pretty simple way red states with contestable races could avoid an electoral catastrophe in November that might result from this issue: don't pass outright abortion bans, and publicly state that they have no plans to. If they have prior abortion bans that are going back into effect now that Roe is toast, such as Michigan has, put the law on hold. The idea is to turn the heat on the issue way down while heating up whatever issues hurt Democrats.
Then, after the Republicans win in November, lower the abortion ban boom.
Then go on Fox, OANN and Newsmax and cackle about how they put one over on the stupid voters.