I think it could avert the Religious Right as it existed IOTL. Before Roe the pro-life movement consisted largely of Catholics who favored progressive politics and saw opposition to abortion as an extension of the civil rights movement, while evangelicals were ambivalent on the issue and many Republicans (included Reagan) supported legal access to abortion. After Roe and with the rise of second-wave feminism in the 1970s, the anti-abortion movement shifted right as part of a general opposition to feminism and "moral decay". With a pro-life Catholic Democrat as president in 1973 we might see a more culturally conservative Democratic Party (a coalition of minorities, labor, and ethnic Catholics) and a more Rockefeller-esque and North/West-oriented GOP.