Jewish (Halachic) law permits and sometimes requires abortion, especially when the life/health of the pregnant person is at stake. Jewish women could sue based on religious freedom requiring the right to abort a pregnancy. Abortion rights may not be guaranteed by the constitution, but religious freedom certainly is.
I’m not a lawyer, obviously, but if Roe vs. Wade gets overturned, then abortion automatically becomes regulated by the individual states or territories.
Of the states and territories where more restrictions on abortion will happen if Roe vs. Wade gets overturned, all of them already have exceptions for the life or health of the mother in their laws. If that’s the case, then no one would ever have standing to bring a lawsuit on those grounds, so it’s kind of a moot point.
In some Satanic groups, abortion is a sacrament, so I guess it’s possible a First Amendment case could be made there. If there’s a Satanic group that practices ritual abortions in a place where it’s against the law, then I think they’d have standing to bring such a lawsuit.
That would, of course, start an argument over just how absolute the freedom of religion really is. Maybe there’s a lawyer here on AM who can actually tell me how right or wrong I am about this.