Taft was a Unitarian.
Then, as now, Unitarianism was equated with atheism by many of the devout, and in a head to head between a progressive Unitarian and freaking William Jennings Bryan, I think the Christian Conservative voter of today would have an easy time choosing. According to Wiki, "Before becoming president, Taft was offered the presidency of Yale University, at that time affiliated with the Congregationalist Church; Taft turned the post down, saying, 'I do not believe in the divinity of Christ.'" Nevertheless, and no doubt with the help of Teddy's coattails, Taft easily won.
Taft was also later president of the Conference of Unitarian and other Liberal Christian Churches, and delivered an interesting address. I guess I usually think of the deist and Unitarian presidents being at the time of the founding fathers and the first generation or so thereafter, but there was one in the 20th century.