I agree with the idea that politics and voting patterns usually have a lot to do with demographics and membership/involvement with institutions that tend to side with one side over the other and therefore in a situation where churches are closer to a left wing party and that left wing party uses a lot of religious themes and rhetoric, that a lot more religious people would vote with the left, with an opposite reaction of secular voters put off by social conservatism.
However, I'm not sure how well a catch-all religious party would really work in the US, religious groups are diverse and also often divided by race, ethnicity ect. There are a lot of Conservative voters who are religious but would ultimately prioritize taxes and guns over their views on abortion.
I kept the current coalitions more intact for my map, I assumed since the Christian Socialist this is based on is Battista Minola, that this party would do best with Catholics, although a smaller number of other religious people also swing left, turning Utah, Mississippi and Louisiana and other states into swing states.