There are quite a bit critics by some extreme leftists on Trump’s comments on Fed policies. The independence of the Fed is an important aspect to ensure monetary policies to be stable and sound without being affected by political thinking that is often short term and biased. However such independence is conditional and not in absolute sense.
First, the Fed should be intellectual so that monetary policies that are conducted are sensible. Looking at the policies they made since COVID-19, none are right and sound, from the characterization of inflation and aggressive interest hikes, to data dependent mentality and reluctant normalization of policy rates. Fed independence is not totally by given, it should be earned as time goes.
Second, Fed independence does not mean they do not listen and take inputs from the public, including the president or other government officers. FOMC members are expected to apply their own judgment but they must take inputs from whatever sources available to them.
The Fed is under dilemma to cut interest rates by 25 basis points or 50 in September when economic concerns mounting and inflation disappearing when housing related components are excluded. Without the clarity of interest rate path, the economy and the market will be hurt.