Why include a small resistance between op-amp stages
The OPA633 has a peak in its frequency response at about 200 MHz of nearly 5 dB when the signal source impedance is 50 ohm. If the source impedance is about 300 ohm that peak is about 1 dB. If you look at graphs in the data sheet you will see this on page 3: -



Using 150 ohm appears to be some form of compromise to avoid too much peaking whilst avoiding too much phase shift. Peaking of a circuit within a closed-loop can cause oscillation and too much added phase shift can do the same so, it looks to me like some compromise has been made with the 150 ohm value to optimize the possibility of the circuit NOT turning oscillatory.

The OPA633 also defaults to using 150 ohm when recommending it to be used inside the closed-loop of other circuits. See this in the data sheet: -