Its been a while since I lowered a mustang and I cant remember if I should keep the rubber piece thats in the center of the spring and re-use it or just trash it?
I figured they were there for a reason (5 cents of rubber x eight zillion stangs = lots of expense).
I figured their purpose related to some noise/resonance/harmonics thing like Joe noted, and like he and Shaker, I swapped them into the Mach 1 springs.
BTW: It's not a "noise" damper, it's a vibration damper.
Like with the damper on rear axle, it's there to eliminate specific frequencies of vibrations. Depending on tolerances, upgrades, bla, bla, bla, it may or may not make a difference.
For those front spring inner damper, there's *no* reason not to use them. For the weight over the rear axle, if someone has a quarter mile ONLY car (that is NEVER used on the street), then removing that rear damper can help reduce the weight. Otherwise, IMHO, the RISK is not at all worth removing the rear damper.
Just because someone has "never had problems before", that does NOT mean that they will never hit bumps in the road under certain weather conditions WILL cause a problem!