Conor Williams makes the case:
The first option looks to religion for substantial political content. Call it “Ideological Religion.” People who approach politics in this way troll their sacred texts, papal encyclicals, past sermons, and other religious documents in search of specific policy preferences. They try, in other words, to build the content of their political convictions from the content of their faith tradition. What, they ask, does the Pope tell us about how to treat criminals? What does the Bible teach about homosexuality? Or our relationship to the environment? Or eating shellfish? Or growing facial hair? Ideological Religion reduces a faith tradition to an encyclopedia of moral information—to find out how to govern, we need only dig up the (purportedly obvious) right positions and bring them to our public arguments. Problem(s) solved, neat and clean! This is, I think, largely what [Amy] Sullivan and many other religiously-minded leftists have in mind when they talk about resuscitating the Social Gospel tradition, etc.
The second option takes religion as a stance for approaching the world. Call it “Dispositional Religion” (an ugly term that I’d happily replace—suggestions?). Instead of looking to their faith for crisp ideological positions, people who approach politics in this way ask a different set of questions: How should a person of faith understand urban poverty? Or God’s Creation? Or the facts of human sexuality? They do not expect that religion provides specific and conclusive solutions to political problems, but they shape their attitude towards human social life in reference to their faith.