The Federalists supported the idea of an independent judiciary while the Republicans (also called the Democratic-Republicans) opposed it. This was because the Federalists were much more worried about excessive democracy than the Republicans.
The Federalists’ main worry was that the US, under the Articles of Confederation, was too democratic. That is, they felt that the mass of people had too much influence over the government. They believed that the masses would tend to demand governmental policies that were good for them in the short term but which would be ruinous in the long term.
Because of this, the Federalists wanted a government that would allow the people to be heard, but would also have ways to mitigate their impact on policy. An independent judiciary was one way to mitigate this impact. If the judiciary were controlled by the elected branches or by the people, it might swing with public opinion and allow laws that were unconstitutional to stand. An independent judiciary, by contrast, would not feel political pressure. It would simply do what the Constitution said it should. In this way, it would be a barrier against excessive democracy. This is why the Federalists favored such a judiciary.