A few considerations. BUIS can be harder to see, and thus use effectively, through a red dot display, especially through something tinted like the RMR. One misplaced drop of moisture, or the wrong sun angle on the emitter, can make multiple dots or even block being able to use the BUIS. Something like the TLR-8G is ideal as it provides an alternative sighting system if the dot’s display is blocked.
I think someone carrying a red dot should practice shooting through pure index, without dots or BUIS, to see what they are capable of with an impaired display.