Haven't seen this pointed out yet. If the scenario is the plane is moving to the right and the conveyor is moving to the left at the same speed therefore the plane is standing still. The conclusion collapses because the first premise, that the plane is "moving to the right", contradicts the conclusion that the plane will sit still.
Anyway, if we look at the real world scenario, the answer should be obvious if you don't get caught in the mental obstacle that tells you the plane will remain stationary for the sake of argument because it won't. Though the plane and the wheels are separate systems conceptually there is a connection with rolling resistance and bearing friction but it's a very small factor.
Thrust is a force which results in a more or less fixed acceleration. Not a fixed speed. This is where a number off you get lost conceptually. Thrust results in a CHANGE in airspeed. Not ground speed. In this case it increases said speed. No fixed pounds of thrust will practically result in a fixed speed along the ground. In order for the conveyor to influence the plane to stop accelerating, the conveyor would need to transmit force equal to the force of the plane's thrust. By the time this would be possible given some outrageous theoretical assumptions, and stupidly high magnitudes, the plane's speed would likely be well above takeoff speeds. This should be enough to get you past that assertion that the plane would remain still.
If we assume that the conveyor could move at a rediculously high rate of speed such that the rolling resistance would cause a force equal and opposite the plane's thrust, the large magnitude of forces would not be applied to the plane along the same point vertically and would likely cause the plane to flip forward due to the torque it would apply to the airframe. Further exemplifying how rediculous it is to consider those components of the argument.
Fine print:
Drag forces and other nonconservative forces will eventually cause a zero net force with increased speed and will result in a terminal speed given a constant thrust. But once again the order of magnitude is too low to keep a plane standing still in a takeoff roll and such conditions would take far too long to play out. Friction of wheel bearings are not influenced by speed on any measurable order of magnitude to matter in this scenario either.
For all intents (TLDR):!The conveyor is moot.