One makes a maneuver count as red, the other makes a maneuver count as green. Do I get to decide which applies? Do they both apply, effectively turning it white?

Sadly, the Red trumps all in this interaction.

Sadly, the Red trumps all in this interaction.

Where is this explained?

FAQ, Page 15:

Q: If two or more game effects that change the difficulty of a maneuver conflict, which effect takes priority?

A: An effect that increases the difficulty of a maneuver takes priority over an effect that decreases the difficulty. For example, if a ship equipped with R2 Astromech is dealt the Damaged Engine Damage card, all of the ship’s turn maneuvers are treated as red maneuvers, including the 1-speed and 2-speed turn maneuvers.