Is there any safety reason that would prevent me from cleaning brass that I already primed? [or any other reason for that matter] I am using dry media.

You might get some residue in the flash hole. Why not just load them and shoot them?

Yep.

They do not have to be "clean"

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Still Running Against the Wind

A long time ago I must have loaded and shot cast bullets with Unique and just put them back in the original styroform box. [the cases were filthy] Yesterday, when I resized them to load again, I was getting sort of a film or like a very light skin of a residue coming off the case. I started to wipe them with a rag but, the cases felt kind of sticky. They are not primed yet, but, I would sure like to clean them again and I know what a pain it is to dig the media out of the flash hole.[made that mistake too] So, hoping that that film will not end up in the revolver cylinder and be more difficult to remove I was hoping I could clean primed cases without any unforseen problems.

Sorry 'bout that. IMHO you're just asking for trouble tumbling primed cases.
If you must clean them, the safe way is to clean them unprimed and then use a primer pocket tool if needed and inspect every flash hole. I really don't want media stuck inside the bottom of a primed case when I load it.

If you only have one box of empties, you can wipe them off with solvent on a rag by hand fairly quickly.

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Science plus Art

Media sticking in the flash hole is not a big deal.........primers are pretty powerful, and that bit of media will be blasted out of there so fast it will be of no consequence in the ignition of the powder.

I've tumbled primed brass on several occasions, then loaded and shot the cases with ZERO ill affects. I consider it a non-issue.

My experience is the same as papajohn428....

Are you willing to bet your gun or your life on that?

I wouldn't be concerned that a bit of corncob is going to prevent a primer flash from going through a hole & igniting powder.

I would be more concerned about a chunk of media preventing the primer from bottoming in the pocket.

FWIW I've found that lizard litter (crushed walnut shell) does not get stuck in the primer pocket like cob. It also cleans more quickly but doesn't give that polished shine of cob & polish.

A lot of people don't deprime their fired cases before tumbling. I do deprime my fired cases before tumbling. This way, the primer pocket gets cleaned. Most resizing dies have a depriming rod and this will expell any stuck media from the primer pocket or flash hole. If you don't deprime your fired cases before tumbling, when you reload the depriming rod in the resizing die will also get rid of any stuck media in the flash hole. The only time that you might have a problem is when tumbling primed cases.....and I agree that is unlikely to be a problem. It's your call, do it the way you want to, I don't think it matters that much. But remember it is smart to inspect cases before reloading.