The Fed is so independent that, according to former Fed chair Alan Greenspan, it is answerable to no one. A chief argument for retaining the Fed's independence is that it needs to remain a neutral arbiter, beyond politics and political influence; and Dudley's op-ed clearly breached that rule. Critics called it an attempt to overthrow a sitting president, a treasonous would-be coup that justified ending the Fed altogether.
Perhaps, but central banks actually serve some useful functions. Better would be to nationalize the Fed, turning it into a true public utility, mandated to serve the interests of the economy and the voting public. Having the central bank and the federal government work together to coordinate fiscal and monetary policy is actually a good idea, so long as the process is transparent and public representatives have control over where the money is deployed. It's our money, and we should be able to decide where it goes.