Are you suggesting that Christians should not be allowed to run for office, or that Christians should not be allowed to vote for Christians? Would you want the same rule for other religions as well?
The fact that they are Christian is incidental. They are not forcing anyone else to become Christian, banning immigrants based on religion, or such. You can preach Islam in the US to non-Muslims, its a constitutionally protected right. Can a Christian preach Christianity to non-Christians in any Muslim country?
Separation of Church and State was originally promulgated by Christians themselves though. The Catholic Church effectively ruled Europe, but dissenting Christians felt that Christianity was a conscious decision, rather than something one could be born into - you had to decide to follow Christ. That being the case, the Church operating as the state and forcing conversions or membership made no sense, and they advocated for separation. Didn't come about till well after the Reformation (the Lutherans were no better than the Catholics on this matter, at the time).
From Wikipedia, about 16th century Anabaptist beliefs that are still influential today: