This _should_ be the difference. The problem is there are a lot of softroaders that are AWD. none of them have an MC classification but the subaru, as far as I'm aware (maybe some of the hyundais?)
The following vehicles have MC classification:
Audi Q5
Bentley Bentayga
BMW X3
Holden Trailblazer
Infiniti QX80
Isuzu MU-X (also available in 2WD which is MA)
Jeep Wrangler
Land Rover Discovery
Land Rover Discovery Sport
Lexus LX570
Mazda CX-9 (also available in 2WD which is MA)
Mercedes-Benz G-Class
Nissan Dualis
Nissan Y62 Patrol
Mitsubishi Pajero
Mitsubishi Pajero Sport
Porsche Cayenne
Range Rover Sport
Range Rover
Ssangyong Rexton
Subaru Forester
Subaru Outback
Suzuki Jimny
Suzuki Grand Vitara (also available in 2WD)
Toyota FJ Cruiser
Toyota Fortuner
Toyota Prado
Toyota LC200
Volvo XC60
Volvo XC70
Volvo XC90
VW Touraeg
The following vehicles are not classified MC:
Jeep Grand Cherokee
Jeep Renegade Trailhawk
Jeep Cherokee Trailhawk
Ford Everest
HAVAL H9
Is it local or state controlled?
I assume you refer to the issue on North Stradbroke Island - the issue is complicated. All National Parks are Federal (National) however, management of certain areas has been placed in the hands of local indigenous Land Councils and I support this. There seems to be a strong move towards strict environmental management principles and although reasons have not been given, my guess is that there has been some concern with ill-prepared campers getting bogged and damaging vegetation by making new tracks around difficult sections. The blame for this has been placed on people using vehicles (AWD) that do not have the ability to stick to the established tracks so the solution is to ban them all.
It is difficult to address this issue while at the same time, demonstrating appropriate respect for the cultural values of the traditional landowners and their capacity to manage the national park in a responsible manner. Knowing who to speak to is also an issue because the person in the chair is not necessarily the one influencing the decisions.
My concern is that what seems like a simple solution in the first instance will be copied in other areas as has already been proposed and eventually adopted nationally as a standard for management of all national parks.
Either way, as Bennie said, it's political. Currently you're dealing with bureaucrats who will just dig in and be obstinate until someone higher up tells them to pull their heads in, you gotta go up the ladder.