Let's cover Unitarians...and just broaden this also to include the historical track record of both Unitarians-as-Presidents as well the usual seven past Presidents identified as "other than what we would recognize today as technically Christian":
George Washington
Thomas Jefferson
James Madison
John Adams
John Quincy Adams
Millard Fillmore
William Howard Taft
(Note: Some also include Abraham Lincoln and Andrew Johnson)
With George Washington and James Madison, I've seen comments from both sides. And many Madison quotes cited by "the other side" are from later in Madison's life. The last four in the list above had unitarian memberships...though John Adams was a Congregationalist growing up and was associated with that church by anybody who may have cared in looking that aspect re: voting for him.
Re John Quincy Adams, he constantly referenced himself as a "Christian" and his diary is filled with critiques vs. liberal Unitarians.
Re: Madison:
Madison's religious views and activities are numerous, as are his writings on religion. They are at times self-contradictory, and his statements about religion are such that opposing positions can each invoke Madison as its authority. An understanding of Madison's religious views is complicated by the fact that his early actions were at direct variance with his later opinions. Consider six examples of his early actions. First, Madison was publicly outspoken about his personal Christian beliefs and convictions. For example, he encouraged his friend, William Bradford (who served as Attorney General under President Washington), to make sure of his own spiritual salvation: [A] watchful eye must be kept on ourselves lest, while we are building ideal monuments of renown and bliss here, we neglect to have our names enrolled in the Annals of Heaven.[1] Madison even desired that all public officials - including Bradford - would declare openly and publicly their Christian beliefs and testimony: "I have sometimes thought there could not be a stronger testimony in favor of religion or against temporal enjoyments, even the most rational and manly, than for men who occupy the most honorable and gainful departments and [who] are rising in reputation and wealth, publicly to declare their unsatisfactoriness by becoming fervent advocates in the cause of Christ; and I wish you may give in your evidence in this way." Source: James Madison and Religion in Public
I've read also a piece entitle, "Was James Madison a Christian or Theist?" -- but the link appears to be dead now.
I think then that the three presidential candidates who were clearly "not" Christian to the voters of their times -- had they bothered to investigate that -- would have been...
...Jefferson
...Fillmore
...Taft
Jefferson: Jefferson was never a member of the Unitarian denomination nor was he ever active in a Unitarian congregation. However, he did once write that he would have liked to be a member of a Unitarian church, but he was not because there were no Unitarian churches in Virginia...[Jefferson] sometimes wrote that he thought the whole country would become Unitarian. He wrote that the teachings of Jesus contain the "outlines of a system of the most sublime morality which has ever fallen from the lips of man." Wrote: "I am of a sect by myself, as far as I know." Source: "Jefferson's Religious Beliefs", by Rebecca Bowman, Monticello Research Department, August 1997 [URL: http://www.monticello.org/resources/interests/religion.html].
Source: The Religious Affiliation of Third U.S. President Thomas Jefferson
Millard Fillmore: For those tempted to say, "Well, Millard Fillmore served as President, and if you aren't willing to vote for a Unitarian, you would have shut out Millard Fillmore."
Well, after his presidency, Fillmore ran for president again in 1856: "He ran for the presidency in 1856 for the Know-Nothing Party, an anti-Catholic, anti-immigrant party."
Source: Millard Fillmore - Thirteenth President of the United States ... If his very party ran on an "anti-Catholic" stance, then who would anybody be to try to use Fillmore as some "anti-religious bigotry" poster boy???
I would say that a solid reason to oppose Unitarians as POTUS candidates would have been (and is still operative, IMO):
... (a) the Christian social ethics of righteousness and justice just didn't carry far into their soul. With Fillmore, his "support of the Fugitive Slave Act caused the Whig Party to split in two and caused the downfall of his national political career." (same source as above) Keep in mind that compromiser British Prime Minister Neville Chamberlain was also raised Unitarian.
...(b) Not only did Fillmore head the "Know-Nothing Party," but Taft as President made the (R) party temporarily into a "Do Nothing Party"...lacking moral force or suasion:
Note this critique even from a Unitarian Universalist source: "The Christian Register, a publication that held Taft in high regard, later commented on his presidency: 'Mr. Taft is not referred to as one of the great Presidents. Two reasons may be assigned: his election depended too much on the will of his predecessor, President Roosevelt; he was temperamentally and mentally unfitted to fulfill the functions of Chief Executive of the nation. He did not enjoy the office, and could not summon the tremendous energy necessary to push through legislation in the face of powerful opposition. He made himself beloved by the people on account of his readiness to smile through difficulties; but that method did not work with Congress, and things simply did not get done." The election of 1912 was a political disaster for the Republicans. Woodrow Wilson easily defeated both Taft and his former supporter Roosevelt (now running for the Bull Moose Party). (So even Roosevelt, who had "anointed" Taft earlier -- had turned against him in 1912).
Source of above quote: William Howard Taft
Oh...and one more thing re: Jefferson: Note that Jefferson is hardly the "poster boy" for "religious tolerance" when Jefferson himself "intensely opposed Calvinism. He never ceased to denounce the 'blasphemous absurdity of the five points of Calvin.' Three years before his death, he wrote to John Adams: 'His [Calvin's] religion was demonism. If ever man worshiped a false God, he did. The being described in his five points is ... a demon of malignant spirit. It would be more pardonable to believe in no God at all, than to blaspheme him by the atrocious attributes of Calvin'" (Works, Vol. iv., p. 363). Source: Thomas Jefferson and religion
BTW, have you critiqued Mormon voters for making "religion" a key sticking point on who they vote for? The Salt Lake Trib said in Feb 08 that the #1 issue among Utah voters was “personal qualities” (We all know what "personal qualities," eh, 7, wink-wink, nudge-nudge). Actually, I'm glad Utah LDS voters voted their conscience & convictions & that they took the other-worldly commitments of a candidate into consideration. It not only shows they are exercising liberty in a Free Republic, but it shows they are just like the Evangelicals above – of whom 92% said they likewise take faith & beliefs into action!
Do not, I repeat, do NOT include me in any of your religious or anti-religious diatribes. I am simply not interested in anything you have to say about anything. Understand?