Because it:

- was created by the US government

- is ran by US government appointees, who are nominated by the President and confirmed by the Senate

- has to make annual reports to Congress

- returns all its profits to the US government

- describes itself as a government agency. [0]

Does the Fed have more independence than, say, the Department of Agriculture? Yes, but an independent government agency is still a government entity.

[0] "The Federal Reserve, like many other central banks, is an independent government agency..." https://www.federalreserve.gov/faqs/about_12799.htm

Because beliefs tend to emerge from ideology as opposed to the other way around. Then those beliefs become the api for interacting with information