It is a matter of whether or not we want to keep Freedom as a characteristic of our nation.
It is Christ who sets Free , who Gives a real Understanding of what Freedom is. A person disconnected from Christ is a slave of one type or another. So, they readily Sacrifice one form of slavery for another.
Christ came to Save the world. He left Christians here to continue his Work. To allow non-Christians to hold office is to invite slavery.
This is why we see people giving up their rights, their Integrity , their votes, their Minds to those who steal for them. The Lie of the left is that it will not be greedy, that it will look after you.
The reality is that SecularHumanism , Socialism , Paganism , Atheism , multi-culturalism, Globalization are different facets of a Philosophy of men, and men (apart from Christ ) have Evil , self-serving Hearts .
So, the answer is 'yes'. Being a Christian - at least in Philosophy - should be a requirement for public office. It represents a qualification that translates to service rather than dominance.
To play on Shakespeare:
To be Free or not to be Free. That is the question.