That election took place in the wake of the French Revolution, which was inspired by the American Revolution but was considerably more violent and intent on overthrowing traditions. The American Revolutionaries just severed the ties to their monarchy; the French actually severed the heads of monarchs. Americans gave themselves freedom of religion whereas the French actually outlawed religion for a time, turning the gorgeous Notre Dame into a temple to the cult of reason. What the American Revolution seemed to be to Britain, the French Revolution seemed to be to the United States.
Jefferson, the Republican candidate, had been in France. He also pushed to create not only freedom of religion but freedom from religion in the US. Jefferson was a Deist who did not trust clergy anymore than he trusted aristocracy, and as a man of science he didn't believe in miracles or God's intervention in daily affairs. The Federalists claimed that a vote for Jefferson was a vote against God and religion, a vote for chaos rather than order, a vote to let the rabble have a dangerous amount of influence. Jefferson was a Jacobin, they said, and a vote for him was a vote to head in the direction of godless France.
Federalists - whose candidate for president was President Adams - had passed an Alien and Sedition Act that let them arrest anyone who spoke against the government. They had argued for laws that would let them - essentially the wealthy elite - vote to determine "the people's" representatives. And, of course, they were horrified that a Deist might hold office. The Republicans argued that a vote for Federalists would be a vote to essentially return to British rule. Not only did the Federalists have ties to Britain but some had actually proposed making the presidency and even the Senate lifetime positions, even allow them to be inherited.
It was not true that Jefferson was so intent on individual liberty at the expense of order and so opposed to religious influence that he wanted the US to be like France, but he certainly leaned that direction more than Adams.
It was not true that Adams was so intent on imitating Britain that he would take away the people's rights and move towards solidifying the hold on power of a new, American aristocracy. (Although curiously his son, John Quincy, did become the sixth US president.) But he certainly leaned more in that direction than Jefferson.
It is interesting how many parallels there are between the politics of 1800 and today. But the one shocking thing that has persisted is that conservatives still don't trust the French. (Remember after the French refused to join us in the invasion of Iraq when members of congress proposed renaming french fries "freedom fries?") These conservatives are still the ones who think that God isn't given His proper due in this country and that the rabble who shouldn't be allowed to vote too easily can and see threats to their traditions all around them.
It's worth pointing out a few things about the hopelessness of the cause of the social conservative, though. Jefferson wrote the Declaration of Independence and is more revered than Adams. Jefferson won the election of 1800, taking the presidency from Adams. Not only did he win but the Federalists proved so irrelevant that their party eventually disappeared. Jefferson had a disdain for tradition but he was only the first in a string of presidents who decided not to wear a sword or powdered wig for his inauguration. And Hamilton - who was head of the Federalist Party and more extreme than Adams - was shot and killed by the Republican, Jefferson's former Vice President, Aaron Burr. Hamilton and the Federalist Party were killed off by Republicans. Social conservatives, however were not. Now they protect the very values and traditions that shocked Federalists and take offense instead at the next wave of social change. Oh, and seemingly still hate the French.