Actually both New Keynesians, Keynesians and Monetarists are advocating for short-run government activism, just the underlying mechanisms are different and Monetarists stress monetary over fiscal policy. According to the New Palgrave Dictionary of Economics (Cagan 2017) monetarism is defined as:
Monetarism is the view that the quantity of money has a major influence on economic activity and the price level and that the objectives of monetary policy are best achieved by targeting the rate of growth of the money supply.
Actually Friedman (1968) and Phelps (1968) criticized the original Philips curve mainly because it posited permanent employment inflation trade-off.
The monetarist Phillips curve would be very close to something like:
$$\pi_t = \pi_t^e + \lambda( \ln Y_t - \ln \bar{Y}_{t}) + \epsilon^s_t$$
where $\pi_t$ is inflation, $\pi_t^e$ inflation expectation $\ln Y_t$ log of current output $\ln \bar{Y}_{t}$ log of the natural rate of output. The argument here is that if government follows inflationary policy and people are not grossly irrational then in the end $\pi_t = \pi_t^e$ and there is no inflation-output trade-off. However, even Friedman himself didn't argued against short-run trade-off. The problem in his view was that in order for there to be permanent trade-off government would always have to 'surprise' people by targeting ever increasing inflation in an unexpected way. However, the moment when the expectations would adjust $\pi_t= \pi^e_t$ and the Philips curve would be 'flat' in a sense output would be orthogonal on rate of inflation as the terms would cancel out.
Thus, if we would argue that $\pi_t= \pi^e_t$ will always hold then there would be no trade-off even in short-run - but that is not really what was ever argued by Monetarists or at least not by Friedman and Phelps. Friedman and co. were writing their research before the rational expectations revolution really took hold so their treatment of how rational expectations work was not really as rigorous as today which probably lead to some misconceptions. I think either this got somehow either not properly explained by the Froyen's book or there is some misunderstanding (I dont know the book So I can’t really comment on that).
Also from your question it’s not clear if the author of your textbook means New Keynesian Philips curve or something like the accelerationist Philips curve.
The accelerationist Philips curve that cab be considered ‘Keynesian’ would look like this:
$$\pi_t = \pi_{t-1} + \lambda( \ln Y_t - \ln \bar{Y}_{t}) + \epsilon^s_t$$
The difference between this Philips curve and the previous one is that instead of inflation expectations $\pi^e_t$ we have there just past inflation $\pi_{t-1}$ (I am guessing that perhaps this is the assumption that was being alluded to in your textbook). This implies that there is always some short run trade-off between inflation and employment.
The New Keynesian Philips curve is yet even more different and given by:
$$ \pi _{{t}}=\beta E_{{t}}[\pi _{{t+1}}]+\kappa y_{{t}}.$$
The New Keynesian philips curve is actually based on ideas of Friedman and Phelps (see Roberts; 1995) where now the mechanism depends on current expectations on future inflation $ E_{{t}}[\pi _{{t+1}}]$. Here there is again always short-run trade-off between inflation and output with a caveat that the trade-off depends on not what past inflation was but what is the future expectation of inflation.
As you can see all three models allow for monetary policy to stimulate economy in short-run but the mechanisms are different:
In the Friedman & Phelps case short run inflation-output trade-off exists when the inflation expectation of people are not correct or if they are being surprised by government.
In the accelerationist case there is always short-run trade-off between inflation and employment because of the assumption of inflation expectations being just past inflation $\pi^e = \pi_{t-1}$.
In the New Keynesian Philips curve the mechanism depends on present expectations of future inflation and there is also always trade-off between inflation and employment with subtle difference that the trade-off depends on what the future inflation expectations are.
I think Romer Advanced Macroeconomics has a good treatment of the Philips curve so if you would like to know more about this that is the source I would recommend.
