Sorry if this has been asked, but I was just wondering how this would be resolved if someone flies through a rigged cargo chute and an asteroid, or a rigged cargo chute and a debris.

Resolve each one in order, one at a time.

7 hours ago, Parravon said:

Resolve each one in order, one at a time.

This. And the order starts with the nearest to your starting position and proceeds outward from there.

Rules Reference, pg. 14, Obstacles: "If a ship moves through or overlaps more than one obstacle, it suffers the effects of each obstacle, starting with the obstacle that was closest to the ship in its starting position and proceeding outward."

Also though, just as a related point, you resolve everything when you fly through it but if you are making an attack through an obstacle the defender only gets one die no matter what.

Essentially attacks are either obstructed or unobstructed. It doesn't matter to what degree.