The letter has been published online as the controversial businessman looks set to become the Republican candidate for the US presidency.
He's all but clinched the job after Ted Cruz bowed out of the race following a defeat in Indiana.
Donald Trump's rise to the top has prompted a "moral crisis in which our faith is literally at stake in the way we respond", the letter said.
It says: "Churches in this country, and our country itself, face such a moral threat today. We are seeing the very worst values of our nation and its history on display with a vulgar message and style.
"A direct appeal to the racial, religious, and gender bigotry that is always under the surface of American politics is now being brought to painful public light."
Donald Trump is fuelling "angry constituency" which is a "threat to both the values of our faith and the health of our democracy", the group argue.
The letter is also signed by Archbishop Vicken Aykazian from the Armenian Apostolic Church and Dr Steve Schneck, the director of the Catholic University of America.
Trump is accused of promoting racial and religious bigotry, disrespecting women, harming civil discourse and offending moral decency.
The letter continues: "Trump's highly visible and vulgar racial and religious demagoguery presents a danger but also an opportunity to publicly expose and resist the worst of American values.
"By confronting a message so contrary to our Christian values, our religious voices can help provide a powerful way to put our true faith and our better American values forward in the midst of national moral confusion and crisis.
The letter acknowledges that many people feel an anger at the way America has been run but says "Donald Trump, a celebrity from the worlds of real estate and reality television, is manipulating this anger for his own political advantage at the expense of the common good".
It says: "Trump is shamelessly using racial resentment, fear, and hatred to fuel a movement against the other, targeting other races, women, cultures, ethnicities, nations, creeds, and a whole global religion.
"His divisive rhetoric, laced with racist, bigoted, and hateful attitudes and wrapped in nationalistic xenophobia, is being enthusiastically embraced by millions, including many self-identified Christians, who are allowing their racial identity to trump their faith. This stands against the truth of the gospel of Jesus Christ."
The leaders stress the letter is "absolutely no tacit endorsement of other candidates".
Meanwhile worldwide evangelist and son of Billy Graham, Franklin Graham, has congratulated Trump on his victory.
In a Facebook post, he said: "We need to continue to pray for major change in Washington and in our country through whoever is elected."
