The vibration can damage the seal on your tranny where your slip yoke slides if the vibration is coming from driveshaft.
To adjust the clutch properly, make sure that there is about 1/4" to 1/8" of play in the end of the clutch release fork when you wiggle it back and forth. No more and no less.
You also shouldn't be getting on the gas with a brand new clutch. Drive it a while to break it in.
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351W 89 Mustang GT Convertible