No it is not normal. Standard geometry for E34's has both anti-dive (when you brake the front does not dive forward and down)and anti-squat (when you accelerate the noe lifts and the back goes down). You should feel the auto engage and very slight movement when going from park to drive. You should not feel the back go dowm. If it does shows wear in shocks and springs and most likely bushes as well. Suggest have you rear shocks removed as well as springs and have both tested. Not too expensive and if within tolerance you know the culprit is something else. But if the suspension is original, this is a good place to start looking due tot he age and wear of these components.
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