To be fair, in the case of abortion, the Courts that upheld those rights were majority conservative, just a different flavor of conservative politics. With the original Roe being won on Texas, it was their SC telling a reactionary AG "no." Then the SCOTUS upheld this using the 14th Amendment.
I dont buy the more modern premise that the right to privacy doesnt actually exist, which I've read in plenty of opposition to Roe, which always dominoes into other decisions like Obergefell where the 14th Amendment at the center. Though I do agree the best legal action is both Court precedent and act of Congress. However the problem with that is always going to be rogue States. And when I say rogue States I dont mean a State where the people are just largely homophobic and dont want gays getting married in their State...I mean States where legislators ignore even the will of the people. Like the ones currently trying to figure out how to get rid of and ignore ballot measures.