Oxygen and carbon dioxide move across respiratory membranes by facilitated diffusion active transport < my guess simple diffusion gated channels

The answer would be Simple diffusion

Oxygen and carbon dioxide could diffuse easily because they not moving against the gradient of concentration. In lungs, the blood from the body is carrying a high amount of carbon dioxide and low level of oxygen. With simple diffusion, the carbon dioxide will be released and replaced with oxygen. Some of the water also comes out if the air is too dry.

Active transport used when the movement of the compound is against the gradient of concentration.