A4 1.8T Quattro shakes on clutch release
 

My Quattro shakes on clutch release, it seems to come from the back of the car and happens regardless of how smoothly I release the clutch. The only time I can't feel it is only on initial start up or when I shift up and down at high vehicle speeds.
I try shifting at 2.5K, 3K rpm and didn't seem to matter much. The mild shake is still there.

I know the car is just open diff so there's not much complicated stuff there.
Could it be a worn clutch? I don't have any shifting issues either. The gears always go in smoothly. Pushing the gas in gently doesn't fix the shake either.

I have 4 tires that are completely mismatch except for the 235/45/17 on the car. Three are summer and one is M+S. Can it cause an issue?