Petroleum based lubricants are generally bad for many of the rubber components on the vehicle. Naturally, there are some components that are designed to accomodate/tolerate petroleum lubricants. I always opt for the silicon lubricants for rubber pieces that are exposed to the elements.
I don't know of any reason why a silicon lubricant should not be used on the various mounting gromets used on the suspension components (such as those of the stabilize bar for example). I have not done that myself and can not comment specifically. I would consult the owner's manual at the very least to see if there are any specific guidelines or recommendations.
Naturally, specific grease specifications are called out for the ball joints, tie-rod ends, etc. Use ONLY the manufacturer's recommendations for these components.