Does protection from a color prevent damage from a planeswalker of that color?

Protection from a color grants four specific shields, remembered by the acronym DEBT: the protected permanent or player cannot be Damaged, Enchanted/Equipped, Blocked, or Targeted by anything with that color. All four shields apply as long as the source of the effect has the relevant color (CR 702.16b).

When a planeswalker's loyalty ability deals damage, the source of that damage is the planeswalker itself, not the ability on the stack (CR 609.7). The planeswalker's color is determined by its color indicator or mana cost as usual (CR 105.2). So if the planeswalker is the protected-from color, the damage prevention shield applies.

It is important to note that protection does not prevent a planeswalker's ability from being activated or its loyalty counters from being removed — it only stops the resulting damage from being dealt to the protected creature or player (CR 702.16b, CR 614.1a).

Concrete example: Your opponent controls Chandra, Torch of Defiance (a red planeswalker) and uses her −3 ability to deal 4 damage to your creature. If your creature has protection from red, that 4 damage is prevented entirely, because Chandra — the source — is red.

This rule applies equally whether the protected object is a creature, another permanent, or a player with protection granted by a spell or ability. The key question is always: does the source of the damage have the color in question? If yes, the damage is prevented (CR 702.16b, CR 614.1a).