They are supposed to but often times these are Democrats campaigning in Protestant Churches, so, no one is really going to do anything about it.
The Protestant Black Church has traditionally been the political seat of power in Black-America as separating the "Reverend" from Al Sharpton or Jesse Jackson from the Democratic Party is nearly impossible.
I was partly--but not wholly--insinuating that.
Like Martin Luther King Jr., Al Sharpton, Jessie Jackson, and well the whole Protestant Black Church Obama joined and appealed to to make his political accession in Black-America and US left-wing politics.
The United States Government is secular but that does not mean it is officially atheist. That would be the former Soviet Union and its ruling communist party. The secular nature of the US Government is that it has no official state church. Like the Church of England.
But if a US citizen becomes a Jewish rabbi or Muslim religious authority or a Greek Orthodox priest... they have a US Constitutional right to run for political office if they wish, and to hold said office if obtaining a plurality of votes.