Technically, any guest that has park passes is entitled to any of the WDW transportation. I have never been asked to show any park passes before, but I guess they can ask at some point.
Just about the only monorail line you may not be able to access would be the resort line at MK. If it's early in the morning, it will stop only at the resorts. Or, if the parks get super crowded, they may ask to see resort ID in order to use that particular line. But that would be the only exception and that doesn't happen very often.