Democratic-Republicans had their opposition Party: The Federalists. And the opposition was pretty heated. Just because their Party name contains the names of the current major Parties, doesn't mean their positions were a combination of current Democratic Party and Republican Party positions.

Gerry was a member of the Party of Jefferson, Monroe, and Madison.

We're flying electric helicopters on Mars yet you can't turn on your clothes dryer in Texas. That's because scientists are in charge of Mars, and Republicans are in charge of Texas.