Another (probably futile) attempt at an analogy.

There's a car in a northbound lane traveling at 60 mph, and a car in the southbound lane traveling at 60 mph. They have no effect on each other.

Now suppose the highway is perfectly straight and the southbound car has an enormous vertical board attached to the left side, miles long. The northbound car has a set of non-geared, free-spinning wheels on its left side. Supposing that both cars drive straight and the wheels remain in constant contact with the board, what happens

Each car travels at 60 mph, the wheels on the side travel at a rate of 120 mph. If they have a standing start and accelerate at the same rate, they still would be able to move in opposite directions and the free-spinning wheels would spin at twice the rate of the drive tires.

Hence, the cars are not "equal and opposite forces" because they are not opposing, just like the conveyor is not opposing the plane.