Yes, but there is a very strong proviso to this.
As Reza Aslan points out, religion isn't just one's sect or one's church or whether or not a person reads their holy book. Religion is an identity. So when we want people to get religion out of politics, all too often we are asking for people not to have democracy.
Still, the way that we allow religion to influence politics is flawed. We allow it to affect public spaces that should be neutral religiously, like posting the Ten Commandment in courthouses (though that picture has improved). We mix in God with money and the Pledge of Allegiance, which is a bit like mixing Skittles and ranch dressing in that it ruins them both.
People should vote based off of their culture, but they should not vote against other cultures. White people in the United States should certainly vote by their values, but they should not vote as a group to try to maintain their power over others. (And, yes, people of color should vote only for what would be actually fair, not what would happen to enrich them).
We need a culture of citizenship, and institutions that project that citizenship. That idea has to say, "I am a Christian, but I vote as an American".