I know you're referring to hardware, but look at it this way - if you add the weight of a driver, passenger, two little people in the back, and some luggage in the trunk, you could easily have 300+ lbs. If you're thinking of hanging 300 lbs. off the rear end (and I'm guessing you are), that might affect the balance and handling.
Mustangs are rated at 1000 lb trailer capacity. Mustang hitches are rated at 2000 lb trailer and 200 lb tongue hitch capacity. This is class I. I have a Curt hitch on my 2019 Bullitt. I installed it myself. It required relocation of the active exhaust wiring and was a significant PITA to install. It is also very heavy. Seeing how it bolts up to the car I would not overload it with the risk of bending the tub of the car. That said, I have trailered about 2000 lbs with it, being careful not to overload the 200 lb tongue weight. I would not load over 200 lbs on a hitch carrier on the car, period. A hitch mounted bicycle rack would be about the max I would use it for.
I no longer pull a trailer with the mustang, as I bought a 2002 Lincoln Blackwood for towing duties. The Blackwood came from the factory with a class IV hitch rated at 8700 lb with an 870 lb tongue weight capacity. I bought a 650 lb rated motorcycle ramp hitch carrier. It weighs 100 lbs. I carried my son's 450+ lb motorcycle from FL to KY on it. The 6000 lb blackwood handling was definitely negatively affected with the extra ~600 lbs on the hitch even though the load was not near the truck's capacity. It was definitely a handful driving it through the big tornado storm we encountered.
I would definitely recommend against mounting anything heavier than a bicycle carrier on the back of a Mustang. Pulling a small trailer under 1000 lbs loaded should be no real problem though.