God never told us what political party we should join. God is interested in what we do and what we believe.
There are some on the Republican side who will tell you that Christian faith is incompatible with being a Democrat, but they're either not thinking it through or they're trying to push party. And, it is certainly in Republicans' interest to convince people about this. Interestingly, the Democrats have been suggesting that Jesus was a Democrat because of giving to the poor and such.
What I look for are politicians who want to maximize freedom. That way I can be free to life my life and others can be free to live their lives. Party is just a way to avoid thinking about who we're voting for, and both parties want us to vote party line, not to think about it. And too many people want to accept that convenient shorthand: "My party good, their party bad."
There are certainly things on the Democratic side that God does not approve of. But, the Republicans have a few as well. That's why we need to look beyond the Republican shorthand of "Gays, guns, and abortion." Parties want power, and I think that's why some of our founders warned against them.