I have the same problem. OP, did you figure out how to remove the spots?

It is most likely dirt being trapped in the nicks in the clear/paint caused by road debris (gravel). On lighter color cars such as white it will first appear as a grey spots getting more and more black over time. Treating the spots with a cleaner will remove the discoloration for a short period of time. The only other option is to add touch up paint or possibly reclearing the whole panel.

I don't believe this is the problem, as the spots are larger than just a nick, with some spots 5-7mm wide. They appear on body panels of the car with and without a clear bra. There is no surface damage to the paint/bra where the spots appear, and the surface of the spots is flush with the paint/bra. Any idea on what products to use? I think it's safe to say I can rule out a clay bar.

Any idea on the cause? Road grime? Some sort of poorly formulated detailing fluid? Acid rain? I'm in SoFL, and to reiterate, I have gray spots on white paint.

Try P21 paint cleaner

I am guessing P21 will not work on the clear bra? Are there any clear bra stain removing products?

If I am understanding you correctly you are not getting grey spots on paint as the OP posted way back when. Instead you are having an issue with your the edges of your clear bra and dirt build up, correct?

If the clear bra was installed correctly then the dirt is not trapped under the edge of the clear bra. I am not sure the best method to remove dirt buildup on the edges of the clear bra without potentially hurting the paint in the process. A bit of elbow grease in the trouble spots during the wash or take a microfiber (after a wash) and use some quick detailer and your finger nail to go along the edges to try and lift the dirt. Again that isn't going to be great for the paint.

Maybe include some pictures of what you are talking about to help troubleshoot.

Sounds like road grime buildup to me in both the OPs and the latest situation. I would try some Adam's APC to see what effect it has on breaking it down.