This is a great question and combines two of my favorite subjects to talk about, religion and politics. It is interesting that the United States is one of the most religious countries in the world and yet we have a policy of not promoting one religion over another. I would argue that we are one of the most religious nations in the world not in spite of our separation of church and state history but because of it. A government that can choose to promote my religion one day is a government that can go against it in the future.
I also feel a special requirement to argue for the religious liberty of others because my religious point of view happens to be the most dominant. It is an unfortunate fact that people judge the message not on the facts of the message itself but on the messenger too. If I was an atheist, an agnostic or someone from another faith tradition, many good intended Christians would write off my insistence of church and state separation simply as someone who is against the gospel of Jesus Christ.
The reason I am so passionately against incorporating my religion into the business of government is that it squarely goes against the teachings of Jesus himself. When Jesus was giving the great commission to his disciples he told them to go and make disciples, to baptize, to teach and for them to obey his teachings and his example (Matthew 28:16-20). In the book of John during the Last Super Jesus tells his disciples exactly how they are to follow his teaching.
"A new command I give you: Love one another. As I have loved you, so you must love one another. By this everyone will know that you are my disciples if you love one another."
John 13:34-35 NIV
Nowhere in the teachings of Christ or in the letters written after his ascension into heaven is reforming the government of Rome ever listed as a priority. Paul never commands it, Peter and John do not either. Not even James, who Protestant tradition hold was Jesus brother, writes a word about the government of their day. Everything that the gospel is focused on his God's grace to humankind and how we are to take that grace and share it with others as freely as it was given to us. In the book of Luke Jesus gives the great commandment.
"Love the Lord your God with all your heart and with all your soul and with all your strength and with all your mind'. And, ‘Love your neighbor as yourself.'"
Luke 10:27 NIV
The call of the Christian message is to be a personal call; it cannot be manipulated or forced on someone. With the "conversion" of Constantine to Christianity all that changed, now the Christian message was not a message but was an Empire. Empires must be defended and enemies must be defeated. This change in mindset led Europe into devastating religious warfare that caused our forefathers to leave their home and build a new nation. This new nation would not be perfect, would struggle to live out the meaning of its creed "that all men are created equal". Our forefathers did this by recognizing the fact that when the government is in the business of religion that the religion suffers and the government suffers too. So while "separation of church and state" is not specifically laid out, its impact on our history cannot be denied.
It is in that spirit and for that reason that I am a firm believer in separation of church and state. Not because I am against my own religion, but because I am in favor of it. Now, you may come from another faith tradition, no faith at all, or somewhere in-between. Know that my commitment is not to use my faith and personal values in your case, but rather to follow the law as it is written and the facts that are presented in court. It is those two things and those two things alone that will decide how my cases will be decided.