After freeing King Awowogei, you can no longer pick the red bananas. When you eat a red banana, you get a message, "You eat the red banana. It's tastier than your average banana."
The red banana can be turned into a sliced red banana by using a knife on it. The sliced red banana is used in the Recipe for Disaster quest to stuff the snake used to free King Awowogei. It has no other purpose than to stuff the king's snake, or to use for food while fighting an enemy.
You can only pick a red banana after investigating King Awowogei in the Lumbridge dining room. You are only allowed to pick one at a time, but more can be obtained through the drop trick.