The nature of central bank policy depends on the economic theories or even political views held by those who control its operations.
Monetarists are primarily concerned with controlling the size of the money supply, not interest rates. They are primarily concerned with avoiding inflation, and may view other economic problems as having their origins in fiscal (federal budgetary), currency exchange rate, trade policy, or other issues, including anything from savings rates to moral hazard. They tend to be non-interventionist unless influenced by political considerations.
Central bank economists who do target interest rates may have a range of approaches. It also matters if they consider the pursuit of full employment or the control of inflation to be the paramount goal.
For my own views on stagflation, and my analysis of central bank and government response, see the thread asking what is the difference between inflation and stagflation, and my recent replies.