Clearly, Jesus would not vote for something like gay "marriage"; however, this issue brings up an interesting question: What question should guide what we do and think?
On the surface, What Would Jesus Do–WWJD–appears to be a good philosophy. And it is if done correctly. However, while Jesus was God our impression of WWJD is not supposed to be our final authority. What we think is based on human reason, thought, and results in , really, making our own god. How do we know what Jesus would do? We have to look to the Bible–the word of God–to really find this out. Since Jesus is God and God cannot commit sin, he would never lie. He would never do anything contrary to what He had already said. If God says homosexuality is a sin in one place, He would not condone it in another. So, done right–looking to the Bible for the answer to the question–WWJD could be ok. If, on the other hand, we base our answer to WWJD on what we THINK Jesus would do, then we have created our own god.
Have you ever read In His Steps? It is a book about a pastor who challenges his congregation to do ask WWJD before they make any decision and the results in their town. The book is in the public domain and you can download In His Steps here.