2003 Mazda 6 Chirping

Chirping typically is from the driver belts. Whether from the stretch-to-fit drive a/c compressor belt to the serpentine belt. Several things can cause chirping: Contaminated belts from oil leaking onto them (or coolant), road debri like very small rock impeded in the belt causing a squeak or chirp when slipping on one the ribbed pulleys, one or more the of the pulley bearings and belt tension can all cause a noise concern.
Does the chirping happen with the a/c or defrost on only? If not, I would suspect the serpentine belt. But if it happens only with the a/c or front defrost on I would suspect the stretch-to-fit belt or a/c compressor clutch.
If you narrowed it down to one of the belts you can spray some water from a squirt bottle onto the belt to see if the chirp goes away if it does then you know its the belt if it does not it may be your a/c compressor clutch. Let me know what you find or if you have any more questions, TY

If it is chirping with a/c on then I would suspect the a/c belt specifically. The bad news it that this particular belt design is different than the majority of belts on the market. It is called a stretch-to-fit belt. That means there is no tensioner to apply tension to the belt. Removal and installation goes like this: remove RF wheel and splash shield to gain access to belts. Install special tool to remove belt from a/c compressor clutch pulley and rotate crankshaft pulley to remove belt. Installation is reverse of the above.

The reason why it is chirping less frequently in park is the engine's pulleys are rotating at a slower speed. When driving it is rotating at faster speed.

It sounds like the belt causing the chirping. If you can get the car to make the chirping noise, get a squirt bottle with water and spray the belt with water if the noise increases or goes away have the belt replaced. Hope this helps, Ty