Should a Presidential Candidate keep their faith and talk of religion out of politics?

absolutely. And some of these guys wouldn't be electable today, due to their non-christian and anti-christian views.
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John Adams (the second President of the United States)
Adams signed the Treaty of Tripoli (June 7, 1797). Article 11 states:
"The government of the United States is not in any sense founded on the Christian religion."

"Twenty times in the course of my late reading, have I been upon the point of breaking out, 'this would be the best of all possible worlds, if there were no religion in it.'"

"I almost shudder at the thought of alluding to the most fatal example of the abuses of grief which the history of mankind has preserved -- the Cross. Consider what calamities that engine of grief has produced!"

"Where do we find a precept in the Bible for Creeds, Confessions, Doctrines and Oaths, and whole carloads of trumpery that we find religion encumbered with in these days?"

"The Doctrine of the divinity of Jesus is made a convenient cover for absurdity."

"...Thirteen governments [of the original states] thus founded on the natural authority of the people alone, without a pretence of miracle or mystery, and which are destined to spread over the northern part of that whole quarter of the globe, are a great point gained in favor of the rights of mankind."
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Thomas Jefferson (the third President of the United States)

"...an amendment was proposed by inserting the words, 'Jesus Christ...the holy author of our religion,' which was rejected 'By a great majority in proof that they meant to comprehend, within the mantle of its protection, the Jew and the Gentile, the Christian and the Mohammedan, the Hindoo and the Infidel of every denomination.'"

"Our civil rights have no dependence on our religious opinions, more than on our opinions in physics and geometry....The legitimate powers of government extend to such acts only as are injurious to others. But it does me no injury for my neighbor to say there are twenty gods, or no god. It neither picks my pocket nor breaks my leg."

"The day will come when the mystical generation of Jesus, by the Supreme Being as his father, in the womb of a virgin, will be classed with the fable of the generation of Minerva in the brain of Jupiter."

"Reason and persuasion are the only practicable instruments. To make way for these free inquiry must be indulged; how can we wish others to indulge it while we refuse ourselves? But every state, says an inquisitor, has established some religion. No two, say I, have established the same. Is this a proof of the infallibility of establishments?"

"They [the clergy] believe that any portion of power confided to me, will be exerted in opposition of their schemes. And they believe rightly: for I have sworn upon the alter of god eternal hostility against every form of tyranny over the mind of man."

"I have examined all the known superstitions of the world, and I do not find in our particular superstition of Christianity one redeeming feature. They are all alike founded on fables and mythology. Millions of innocent men, women and children, since the introduction of Christianity, have been burnt, tortured, fined and imprisoned. What has been the effect of this coercion? To make one half of the world fools and the other half hypocrites; to support roguery and error all over the earth."

"In every country and in every age the priest has been hostile to liberty; he is always in alliance with the despot, abetting his abuses in return for protection to his own."

"Fix reason firmly in her seat, and call to her tribunal every fact, every opinion. Question with boldness even the existence of a God; because, if there be one, he must more approve of the homage of reason, than that of blindfolded fear....Do not be frightened from this inquiry by any fear of its consequences. If it end in a belief that there is no God, you will find incitements to virtue on the comfort and pleasantness you feel in its exercise and in the love of others which it will procure for you."

"Christianity...[has become] the most perverted system that ever shone on man....Rogueries, absurdities and untruths were perpetrated upon the teachings of Jesus by a large band of dupes and importers led by Paul, the first great corrupter of the teaching of Jesus."

"...that our civil rights have no dependence on religious opinions, any more than our opinions in physics and geometry."
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James Madison (the fourth President of the United States)

"Religious bondage shackles and debilitates the mind and unfits it for every noble enterprise....During almost fifteen centuries has the legal establishment of Christianity been on trial. What have been its fruits? More or less, in all places, pride and indolence in the clergy; ignorance and servility in laity; in both, superstition, bigotry, and persecution."

"Religion and government will both exist in greater purity, the less they are mixed together."
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Benjamin Franklin

"My parents had given me betimes religious impressions, and I received from my infancy a pious education in the principles of Calvinism. But scarcely was I arrived at fifteen years of age, when, after having doubted in turn of different tenets, according as I found them combated in the different books that I read, I began to doubt of Revelation itself."

"...Some books against Deism fell into my hands....It happened that they wrought an effect on me quite contrary to what was intended by them; for the arguments of the Deists, which were quote to be refuted, appeared to me much stronger than the refutations, in short, I soon became a thorough Deist."
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