How was Jefferson both inclusive and exclusive of the federalists?

In a way, Jefferson was inclusive of the Federalists in that he allowed the party to remain in existence. While the election of 1800 soured the relationship between Jefferson and Adams, the Federalist party was not purged after the election of Jefferson. This was unique in world history because the losing power often was destroyed. Even though Jefferson cut the size of the military budget, he allowed many officers with Federalist leanings to stay at their posts. Even though Jefferson was a strict constructionist, he did authorize the Louisiana Purchase without the approval of Congress. While some Federalist newspapers disagreed with this because the money would help France, most people agreed that it was a great thing to expand the national borders.
Jefferson excluded against the Federalists when he formed his own Cabinet. One of the most famous Anti-Federalists, James Madison, served as Jefferson's Secretary of State. This powerful position made Madison a logical choice to be Jefferson's successor. Jefferson passed the Embargo Act in 1807 over the protests of Federalist strongholds in New England. This action prohibited American shipping with Britain and France, but it hurt New England merchants the worst due to their dependence of trade.

In 1800 the United States had its first real, competitive presidential election when Thomas Jefferson of the anti-Federalist Democratic-Republican Party ran against John Adams of the Federalist Party.
While it is true that Jefferson was generally skeptical of a strong, central government—expressing distrust of Alexander Hamilton's proposal for a National Bank—he was more opposed to the Federalist Party itself than to the concept of federalism. After the end of his presidency, Jefferson wrote, "I have been ever opposed to the party, so falsely called federalists, because I believe them desirous of introducing, into our government, authorities hereditary or otherwise independant [sic] of the national will."
On many occasions Jefferson could be found adopting policies inclusive of federalism by advocating for a strong, central state. He extolled a common identity for the people of America and pushed the early republic into the Tripolitarian War. Afterwards, he established by the U.S. Navy as a permanent military force under federal control.
https://isi.org/intercollegiate-review/thomas-jeffersons-federalism-1774%e2%80%921825/