It's not all BS. There are greases incompatible with other types but you are unlikely to have the problem with the standard over-the-counter brands.

That said, why not give the bearings a decent cleaning and add all fresh grease? You don't have to get them surgically clean, just wipe off as much of the original grease as you can and replace with fresh stuff.

Automotive grease is fine but lithium based lighter greases are usually the recommended type for bike bearings.