‘Chugging?’

be to take a close look at A/C performance, checking high and low side system pressures. Your Taurus uses the cycling clutch and orifice tube method to regulate pressures rather than a thermal expansion valve. This means the system goes full blast, cycles off, then goes full blast again as needed, rather than the compressor remaining on continually with gradual pressure regulation, as in many other cars.

Frequent cycling, as you've mentioned, could be caused by low refrigerant level or a faulty pressure switch, and can play hell with idle stability. Each time the compressor cycles off, idle speed increases, as there's less engine load. Each time the compressor engages, the engine grunts slightly, hopefully softened by a quick and smooth idle speed increase.

Your term "chugging" is interesting, as it infers the engine might be laboring as the compressor engages, or perhaps builds pressure. This could go back to the engine being slightly unhappy or the A/C system working it excessively. Should the condenser cooling fan not be functional or effective, this makes the compressor work harder, loading the engine more than normal. This would be inconsistent however, with the previous guess of low refrigerant level.

Your thoughts of a faulty belt, faulty belt tensioner, or loose or cracked compressor mounting bracket or bolts are spot on. These possibilities should be considered during an initial visual and performance inspection. Other possibilities include a faulty engine mount or A/C metal lines vibrating or making contact with adjacent parts, such as the Taurus' body.

Ford and many other manufacturers coin this as a noise, vibration, harshness— or NVH— issue. They can be quite a challenge to fix. A service bulletin search, another thing to do at the beginning of diagnosis, pointed to possible issues with an imbalance in the condenser fan's cooling fan blades. This can cause rumbling or shaking when the A/C is selected. Since your car operated smoothly for almost ten years prior, blade imbalance is unlikely, but damage to fan blades or a tight or seizing fan motor are possible suspects.