Is it bad to cycle between different driving modes while the car is moving?

If you define driving mode as ECO or NORMAL or SPORT ...the answer is no ...no harm done , if you define driving mode as EV or HV or CHARGE or AUTOEV the answer is no ...no harm done.
the car wont let you harm it

 

Doesn't matter. Switch at will. They are just electronic control settings.

 

+1.

 

Shifting between D, N and R is a little trickier. If you’re above a certain speed (say 5 mph) the car’ll ignore you if you try to go from D to R. I think…

and below the speed threshold shifts like that are best avoided. I have gone from R to D when “almost” stopped; it took it in stride.

 

In a gen 3 (I'm assuming gen 4 is similar), if you try a shift at higher speed than the car likes, it will double-beep and go to neutral instead.

Any shift it lets you make is ok; it knows its limits.

A shift to P at a higher allowed speed may make more of a bump than you like, when the transmission locks. I prefer to be stopped when shifting to P.

Shifts between D and R and vice versa are perfectly smooth. The car just starts pumping electrons one way instead of the other.

The worst risk of making such shifts in a Prius is you might form a habit you then try to repeat in some other car.

 

After the infamous Runaway Toyota fiasco, I tried all those shifts at various speeds as possible means of escaping the alleged surging or runaway engine, and found exactly what Chap describes above. D-N-R, no problem, in fact at highway speed D->R was as even faster way to get to N than a deliberate shift to N. A deliberate N shift has an imposed delay, requiring the driver to hold it there for a bit, whereas attempting R resulting in immediately going N with the double-beep warning. I practiced this occasionally, trying to build a bit of reflex muscle memory to replace the clutch foot reflex that actually did stop a fatigue-related pilot-induced engine surge many years earlier.

Attempting to Park at highway speed did the same thing, though since it requires eyes to find the button, is slower than a feel-only R move of the shifter. At much lower speed, yes, I did get one just under the threshold speed such that it engaged Park instead of overriding to N. The car was fine, but it was more jolt than I personally wanted.

On older models, pressing and holding down the ON switch for several seconds was another way to shut down or escape an alleged runaway engine, in Prius and other push-button Toyota models. After the CHP tragedy, Toyota programmed newer model years to also recognize repeated rapid stabs of the ON button as another panic shutdown method.

My new RAV4 Prime Owners Manual says that for emergency shutdowns, it recognizes holding down the ON button for 2+ seconds, or pressing it 3+ times in succession.

 

Great ! BTW I meant POWER mode instead of SPORT mode in my post

 

Technically it’s PWR mode.