The obvious?

It would seem that - in a functioning democracy based on the principles of religious freedom and liberalism (so, not America) - that a choice to take on a proselytizing role in a specific church would preclude you from serving in public office. You chose a position that stands in direct opposition to the established principles of the organization (and people) you want to be elected to represent.

BEING religious is not a disqualifying factor. Your belief system is yours, and should not eliminate you from running for office.

Choosing a role that specifically promotes one religion over others, shows you do not hold the core foundational values of this country as your highest guidepost, and therefore you should not be able to take on a role representing that set of values. The internal conflict should be obvious; Are you here for America or for God? At some point you will have to choose one over the other, and when in elected office representing a plurality of beliefs, you must ALWAYS put the American ideal over your religious beliefs.

And if you choose the American ideal over your religious belief when push comes to shove, then you are failing in your role as a promoter of your religious views. So you are failing your promise to your congregation.

A clear conflict of interest should be a precluding factor for running for office. The Emoluments Clause is just one of the better known principles that further reinforces the idea that an elected official needs to serve the office first, and other interests second.

"Well then, I'm a Communist/Nazi and want to destroy America. Can I run for office?" I hear you ask...

Sure! And no, I don't know why this is different. So sue me.