Those people tend to adhere to the "emerging Church" school of Christianity, which combines evangelical views on social issues with progressive views on economic and environmental issues. It's kind of like liberation theology but for First World white people who don't really have anything to be liberated from.
You couldn't get on a major party ticket to begin with. Republicans wouldn't want someone so unfriendly to oil and mining companies. Democrats wouldn't want someone so fervently anti-choice.
Hey now I am pro-choice. If there are pro-choice Catholics there can be amongst us too.