The political tensions after the election of 1796 primarily increased because the elected president and vice president were from opposing parties. John Adams, a Federalist, became president, while Thomas Jefferson, a Democratic-Republican, became vice president. This unique situation created a conflict in governance, as the two men had fundamentally different views on the role of government and policies, leading to heightened political divisions and partisanship in the early years of the American republic.
While other points you mentioned may reflect aspects of the political landscape or individual sentiments at the time, the direct cause of increased tensions post-1796 is largely attributed to the party division at the highest levels of government.