Is there a part of the rules for helping cards "forget" things?

The rules don't "forget" a chosen color, but rather than just refering to "the chosen color", you can instead refer to "the last chosen color" to make only the most recent choice matter.

Reference: Chromatic Armor.

As a design note: I think it is better to choose the color as you attach the Equipment and adjust the equip cost accordingly. It's also less text since you don't need separate abilities to choose colors on ETB/unattaching.

Outside of that tapping the Equipment is weird here.

People often tap the equipment when they tap the creature, which adds confusion. I like SI's suggestion to make choosing the color happen when you equip this. What about:

"Whenever you equip ~ to a creature, choose a color.

Equipped creature has protection from the last chosen color.

Equip "

Like that?