In theory, no, but given the deep, deep religious background of America, we're probably one of the few countries - maybe the only one - where the two could potentially intermingle; just look, for instance, at the power (or supposed power, depending on perspective) of the Evangelical Community at present. Reading the question again, though, reminds me of a retort the Left has begun to throw at evangelicals: if you're so pious and godly, how could you vote for a thrice-married adulterer such as Donald Trump for President?
I was asked that question recently myself and my answer was simply thus: "Because no one was voting in 2016 for a pastor in their church or for an elder or deacon or bishop; they were voting for someone for a political office and when compared to his opponent, Trump was the better candidate, warts and all." I think of it like this: there are times where God sends us a person to lead us who doesn't fit the mold of a godly leader but whose actions are most certainly righteous and godly for their time and day.
One example, though not political, is that of Ulysses S. Grant. the man, was, pre-Civil War, a bit of a failure: finished near the middle of his class at West Point, served w/out distinction in the West and then in Mexico during the Mexican-American War, was a bit of a drunkard and swore very copiously yet when the most successful military commander on the Union side during the war. Indeed, when Lincoln was told the man loved a taste of the grape (i.e. drank) he asked for numerous barrels of whatever it was Grant drank to be sent to his other generals so that they could fight like Grant. In addition, when asked to replace him w/some Washington bureaucratic general, Lincoln is said to have opined about Grant - "I can't spare this man; he fights."
