engine air filter yes. cabin air filter still yes.

Yes, your car needs clean air intake and if your filter is dirty it can’t get clean air. Dirt roads and trash off the roads can make your air filter dirty. And by not having a clean air filter your car will run ruff.

if you are talking about the engine air filter yes you do, it has nothing to do with the air conditioning. if you are talking about the in cabin air filter, the manufacturer recommends replacement once a year it filters the air if you use the vents, air conditioning or heat, so yes again.

The air filter is not related to the air conditioning. It filters the air which flows into the engine. You should replace it at the manufacturer suggested interval or when it gets reasonably dirty.

The filter for the cabin air (air con, heater, vents) is often called a pollen filter and it filters the air which comes into the passenger compartment. It does this all the time, not just when the air conditioning is on. This should also be replaced at the manufacturer recommended interval.

Your vehicle may not have a pollen filter but all vehicles have an air filter.