Tail pipe rattles when AC is on

The refrigerant compressor attached to your motor via rubber belt adds load to the engine. This in turn can lower your engine RPM, causing an object to reverberate as the frequency matches it's length or is otherwise able to excite the material, similar to a guitar's string. That's the rattle. It could be any part, any piece, and anywhere on the car, as different materials absorb different frequencies, and it's extremely hard to pinpoint rattle noises unless you can cause the rattle yourself without the car running. The best way to find the rattle is to cause it to happen and work around the car touching things until it stops. (Careful, many things on a car can severely injure you if not approached with care and common sense, especially while the engine is spinning.)

The other possible cause is the compressor itself may be on its last legs if it never shows up anywhere else. Adding refrigerant with one of those cheapo DIY kits is a great way to destroy the compressor as you can accidentally introduce moisture into the system and cause rusting/corrosion inside both the compressor itself and inside the plumbing that holds it all in.

And finally, refrigerant compressors require a fine mist of oil at all times to not destroy themselves. If a hole has formed somewhere, even a small one, the oil could have leaked from the system and adding cheap R-134a (without any oil) could also make it sorta knock and carry on until it destroys itself.

Hopefully, this helps somewhat, and you locate the rattle as being something simple and of non-concern (which little squeaks and rattles almost always are...).

Suggesting an answer as I don't have enough rep to comment. In the same vein as Jimmio's answer, when the AC is on it's probably creating resonance along the exhaust due to RPM shifts.

I actually had a very similar issue, I'd get a rattle at very specific RPM ranges from the back of the exhaust. My issue turned out to be several slightly separated exhaust hangers. Visually they looked normal however when you moved the exhaust they weren't attached but rather held on by the pressure provided from the remaining hangers. You generally want to get hangers fixed as an exhaust falling off is a bad day for everyone - any exhaust shop can do the welds pretty quickly and cheaply assuming that's what the issue is.

If you live in an area that uses salt during the winter then it is very possible they just degraded over time. In my case, I had an aftermarket stainless steel exhaust that must have had the hangers welded on by a blind person. So this may just be an anecdotal answer, but it's generally something that could get overlooked.