Unlike some of those above, i think a different Roe is possible. You would likely have to have different justices, but if 2-3 were opposed, it means one can easily find justices that vote differently.
As an atheist, I can still find a long list of clearly religious motivated laws that should be struck down.
1) Buying beer on Sunday.
2) Prostitution is illegal.
3) Gambling is still only partially legal. For example, if I played a game of poker in my house, I could be arrested and go to jail for many years.
4) Gay marriage.
5) Islamic marriage/more than one wife - Seriously, what is the societal harm from 1 man and 2 women wanting to form a family.
6) Zoning laws in relationships to strip clubs and like being near churches, schools, and etc. I understand making strip clubs go into light commercial districts. I am even ok if you make go light industrial (M class zoning). But this XXX feet from a church is clearly religious based.
7) Sex laws. I have not check in years, but I am pretty sure anal sex among married couples is still illegal in many states. Maybe oral.
8) And on sex laws, why do married people get to do more activities in some states?
9) etc, etc. This could go on for pages.
Now as to the political impact of the supreme court refusing to fight, it would be a state by state battle where the pro-abortion forces normally win. For example, Mississippi had more abortion clinic pre-Roe than today. It is only such a constant issue because the pro-abortion forces know they can basically ignore. If you are middle class, even in a state with no clinics, you just have to take a trip once in your life for the abortion. Small bother. To the other side, it is murder. Now the strange thing is that so would be many birth control methods such as the IUD that impact post fertilization events.
And shouldn't this be in the political tab?