I think you can make pragmatic and tentative choices of party as a Christian, but Christian ought to be, in an important sense, independent of any party. Parties are coalitions that combine godly and ungodly interests, almost by definition.
A great but neglected Lewis essay is one called Meditation on the Third Commandment. When I was writing a column in the bulletin for the church I worked at back in 1980 (!) the Moral Majority was just taking shape. I wrote an essay in which I basically cribbed Lewis's essay to argue that the Moral Majority was a misguided enterprise.