In the year 1800, what shared beliefs and experiences between the Federalists and Republicans allowed the Republicans to keep the nation together?

In the year 1800, you might have thought the US would become
divided between the Federalists and the Republicans.  This was, after all, the time of the Alien
and Sedition Act by which the Federalists tried to prevent the Republicans from exercising their
right to political speech.  However, I would argue that a shared belief in representative
government and the shared experience of the Revolution helped keep the nation
together.

You have to remember that, at this point, many of the
political leaders in the US (in both parties) had worked together to create the Declaration of
Independence and/or the Constitution.  They had been together during the struggle for
Independence.  This meant that they shared a common dedication to the ideas embodied in the
Constitution.  It also meant that they had been comrades during a very trying time.  Both of
these things evidently meant enough to the two sides to keep them from really splitting into
sides that were openly "at war" with one another.