Is it safe to clean a PC with a shop air compressor?

You can use a compressor, but I wouldn't assume the air is clean just because the surrounding climate is dry. Compressors can collect water, and some systems can also carry oil into the air line.

Drain the tank and use a suitable filter and dryer downstream. Check what comes out of the hose before pointing it at electronics. Draining the tank alone doesn't guarantee the air is dry or oil free.

Pressure matters too. Turn it down and use short bursts rather than blasting components at full force. A strong jet can dislodge small connectors or damage delicate parts.

Shut down and unplug the PC first. Hold the fans still while cleaning them so the air doesn't spin them excessively, and be gentle with the blades.

If you can't verify the shop air is clean and dry, I'd skip it. An electric air duster is a reusable alternative, and a can of duster works for occasional cleaning.

With canned duster, follow the can's directions and keep it upright to avoid spraying liquid propellant onto the computer.

Static discharge is another concern around exposed electronics. Power the machine off and unplug it, avoid touching components unnecessarily, and take normal static precautions while working inside the case. Clean air and moderate pressure don't address that risk by themselves.