If it only shakes in drive at a stoplight, and putting it in neutral stops the shaking, then it just sounds like the idle speed is too low. The drag of the transmission lowers it just enough for the rough idle to be perceptible.

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2007 X3 3.0si, 6 MT, Premium, White

Retired:
2008 535i, 6 MT, M Sport, Premium, Space Grey
2003 X5 3.0 Steptronic, Premium, Titanium Silver
2002 325xi 5 MT, Steel Grey
2004 Z4 3.0 Premium, Sport, SMG, Maldives Blue