Most airplane pilots are aware of P-Factor in propeller driven aircraft and that it tends create a torque in phase with the lift imbalance over the blade disc, resulting in a yaw moment about the airplane's CG. Curiously I'm surprised that it does not act to cause a pitch up moment as one would assume that to be the result of gyroscopic precession acting 90° out of phase with the application of the reaction forces. This occurs that way with the retreating blade lift imbalance in helicopters leading up to a retreating blade stall if the airspeed is high enough through the rotor disc. Retreating blade lift imbalance is a result of lower relative wind speeds passing over the retreating blade than the advancing blade. But instead of resulting in a rolling moment towards the retreating side of the rotor disc, it results in a nose up pitching moment due to gyroscopic precession. Which raises the question: Why is gyroscopic precession present in a helicopter rotor due to lift asymmetry over the disc but absent in a propeller? Gyroscopic precession causes phase shifts in resultant forces on propellers when the propeller disc is pitched or yawed in aerobatics or tailwheel aircraft operations, but P-Factor does not cause this as well?
Related, especially footnote 2: What is the influence of yaw on P-factor?
The answer to your specific question is that when you are talking about the effect of P-factor on a prop, you aren't talking about actually moving the prop disk in pitch or yaw. You are applying a rudder force as needed to prevent that movement, so there's no gyroscopic effect to consider.
Whenever the prop disk is actually pitching or yawing-- regardless of whether the cause of the movement is P-factor or something else-- then you have to consider the gyroscopic effect, which makes the force act as if it is applied to the blade disk at a point 90 degrees further along in the direction of rotation.
In helicopters, the individual blades can be moving in a way that creates the same gyroscopic effect as pitching or rolling the entire blade disk, even when the blade disk as a whole is not pitching or rolling. This is due to the way the blade is hinged. This wouldn't happen with a rigid rotor disk. So that's why-- at least with a hinged blade system-- the P-factor effect acts 90 degrees further along in the direction of rotation from the point where it is actually applied, even when the body of the helicopter isn't pitching or rolling, and even when the circular path traced by any given rotor blade tip is remaining constant over time.
$\begingroup$ Check this answer carefully; your mileage may vary-- $\endgroup$ Feb 17, 2021 at 22:19
$\begingroup$ I think that's about right. Precession will introduce a pitching moment that skews the resultant force only if you ALLOWED P factor to yaw the plane. $\endgroup$– John KFeb 17, 2021 at 23:30
$\begingroup$ A “rigid” rotor allows blade flapping just like a hinged or teetering one does, just via flexing rather than hinges. But it does indeed transfer some torque directly, so the control forces act a bit less than 90° further, but still at least about 70°. $\endgroup$ Feb 21, 2021 at 8:34