This is what I understand "standard" monetary theory to say about the relation between inflation and nominal interest rates.
I want to distinguish two cases.
In the first case the central bank pegs the time-path of the money supply. The money supply is exogenous. The nominal interest rate is endogenous. Standard monetary theory says that a permanent 1 percentage point increase in the growth rate of the money supply will (in the long run) cause both the nominal interest rate and the rate of inflation to rise by 1 percentage point. The Fisher relation holds as a long-run equilibrium relationship. The real interest rate is unaffected by monetary policy in the long run.
In the second case the central bank pegs the time-path of the nominal rate of interest. The nominal interest rate is exogenous. The money supply is endogenous. Start in equilibrium (never mind how we got there). Standard monetary theory says that if the central bank pegs the time-path of the nominal interest rate permanently 1 percentage point higher, this will cause the price level, and the rate of inflation, and the stock of money, to fall without limit. The Fisher relation will not hold, because there is no process that will bring us to a new long run equilibrium. The real interest rate will rise without limit.
These two cases are very different, because a different variable is assumed exogenous in each case.
I am assuming super-neutrality of money, in long-run equilibrium. The Fisher relation is a long run equilibrium relationship. We never get to the new long-run equilibrium in the second case, and so the Fisher relation does not hold.