"It has been suggested to me to take an extra air filter and swap it out as soon as you drive off the playa"
Most people drive in Gate Road, find their camp, park their car, and it stays there for the rest of the event and doesn't run. Your air filter should be fine unless you are actually driving the vehicle during the entire event, then yeah, replace it.
So we have a big dust storm. If the vehicle isn't running, then there is no problem. No dust, or very little, is getting into the air filter.
Of course the correct answer to the original question is "obsess".
Do you think the people who live in Gerlach and Empire change their air filters every day? Sure, they change them more often than someone in SF does but come on. You are going to make one ride in, one ride out, that's it. If the car is not running, it is not sucking dust in.
Pabst Blue Ribbon - The beer that made Gerlach famous.