Can you activate a planeswalker loyalty ability at instant speed in response to a removal spell?

Loyalty abilities are a special category of activated ability, but they come with a strict timing restriction. Under CR 606.3, a player may activate a loyalty ability only any time they have priority during their own main phase, and only when the stack is empty. This is the definition of "sorcery speed" (CR 307.1).

This means that once an opponent has cast a removal spell targeting your planeswalker — putting it on the stack — you no longer meet the requirement of an empty stack, and it is also no longer your main phase moment where you could have acted freely. You simply cannot activate a loyalty ability in response.

Additionally, CR 606.4 reminds us that a player may activate a loyalty ability only once per turn, and only if no other loyalty ability of that permanent has been activated that turn. So even under ideal timing, you are limited to one activation per turn.

Concrete example: Your Gideon of the Trials is on the battlefield. Your opponent casts Hero's Downfall targeting it. You cannot tap — metaphorically — and activate Gideon's +1 or any other loyalty ability in response, because the stack is no longer empty. Your only option is to respond with instants like Negate if you have them.

The takeaway: always activate a planeswalker's loyalty ability before your opponent gets a chance to cast removal, or accept that once they've cast it, that window is gone.