Actually, there is a way to do this without adding a complete copy of the player sprite.
Add a new sprite to your game. Make it a red box large enough to cover your entire player sprite no matter what animation is playing and set its effect to "Destination Over". Add events to center it on the player sprite and make it follow it. Also make sure to have it be in front of the player sprite.
Now, when you want to make the player sprite red do this.
+ Whatever conditions you need to make it red
- Player Sprite: Set effect: Destination Out
- Red Box: Set Visible
- Player Sprite: Set effect: None
- Red Box: Set Invisible