OK, for everyone experiencing grinding/noisy brakes, especially at speeds of 20mph and under:
This is NOT a Mazdaspeed Protege specific problem!
Since aesbestos(sp?) can no longer be used brake pads, Mazda has been continually testing new brake pad materials and compound combinations. Because of this, different Proteges have different pad compounds. It depends on a slew of factors, but mainly on production order. For example, Mazda sends all Proteges built within one month out with compound A and the next month they use compound B.
The compounds are tested before installed onto public production vehicles, so don't think Mazda is just slapping them on and sending them to dealers without testing. Obviously their goals with new pad materials are greater longevity, resistance to heat, resistance to glazing, harder bite etc. There are however some negative side effects. One of these is low speed noise/grinding. The noise can even be more prelevant when wet, depending upon which compound you have.
Is this annoying? Of course. Is this a safety concern? No. Will replacing the rotors and pads fix this? Unlikely as once the new pads have been bedded in properly the noise will return.
How do you fix the problem? Turn up your radio, buy some aftermarket pads(Carbotech's for the MSP), buy a big brake kit or just learn to deal with it; except it as another little quirk.
Let me end by saying once again that the noise REALLY sucks and gets annoying, but its nothing an "active" drive can't fix. Every car has issues, you just have to learn to cope with them. Easier said than done maybe...