Going for a bit of an unorthodox position; retain the New Deal Coalition, and have it end up subsuming the Evangelical movement instead of the GOP, leading to a more conservative but still economically center-left/populist Democratic Party that's heavily influenced by Catholicism and Evangelical Protestantism.
I would wager that most Americans - let's say 80% - really don't care one way or the other about abortion as an issue, and only really have opinions on it because it's become a proxy war between the two parties. Therefore, I would guess that many, if not most, Democrats vote for that party not due to their support for abortion, but rather because they have traditionally been perceived as the party of the working class in opposition to the Republicans, who have been perceived as the party of the business elite. If the Democrats were pro-life and the Republicans were pro-choice, I suspect that support for abortion would become tainted as something associated with the interests of the elite, especially if they lean more into economic considerations for abortion, whereas the Democrats would be viewed as the party for working families, not only working to restrict abortion but also ensuring that Americans have the means to support families. In more recent years, this dynamic could even lead to opposition to abortion being considered a major cause for social justice, with this already being an OTL talking point among pro-life Democrats and various Christian democratic movements. This more populist move could in turn give the pro-life movement even more of a boost than IOTL, and potentially even lead to legislation like a Human Life Amendment being passed.