Are the Federal Reserve and the ECB still independent central banks?

There are two levels of analysis: Is the central bank actually independent or is it forced to act by government? Did the Federal Reserve cut its interest rates because Donald Trump asked it to? Will the ECB lower its interest rates to prevent a fiscal insolvency crisis caused by more expansionary fiscal policies (for example in France and Italy)? Does the functioning of the economy allow central banks to be independent? For central banks to be independent, there must be no need to coordinate monetary policy with other policies, in particular fiscal policy - i.e. monetary policy must not give rise to an externality for other economic policies. But monetary policy interferes with fiscal policy, since it makes countries solvent that would otherwise not be solvent if it were more restrictive, and because it still has an influence on real interest rates. Monetary policy and fiscal policy should therefore be coordinated, which is incompatible with the notion of central bank independence.