How are insects and arachnids kept out of commercial passenger airliners?
Like anywhere else, they only become a problem if they affect safety. That is why things like pitot probes and static ports are covered to prevent insects like  mud-daubers' from building their homes inside. Depending on the area it could only apply if the aircraft is not flying for x amount of time but in areas where these insects are very active it could be required for shorter transits. The recent Malaysia Airlines case (Brisbane, Aust) where the pitot-cover was not removed before flight was a case where the covers were place for a short transit because of these insect activity.

If the destination country has laws in place where the entry of non local insects is not tolerated they may require the airline to spray the holds before departure. I remember doing this for flights to Australia. We had cans with a 'lock' trigger (continues to spray without finger pressure) which we would activate and leave in the holds before closing the doors. It was important to notify the crews beforehand as the mist could activate the smoke detectors.