This is a great question, and GotQuestions has provided a solid answer here. I also found the following video which explains it pretty well.
Basically, both sources argue that the separation of church and state is a wise decision. It protects the integrity of the church and the religion freedom of individuals. That being said, this does not mean individuals of religious faith should not be involved in politics. It simply means that people - regardless of religious belief (including Christianity; including atheism) - have the opportunity to voice out their opinions in the public sphere.
[Answered by Pastor HM]