First, "Airbag Compatible" aftermarket bumpers do not directly indicate any special design of the product - rather it only indicates that a vehicle has been crash tested with the bumper installed and found that there was no significant change in the way the airbag deployed as compared to stock. Companies like ARB do go an extra mile to crash pulse test and add special components to their bumpers which allow them to perform off-road while making few compromises in the safety features automakers have designed into their vehicles.
Second, most airbag sensors are basically accelerometers which close a contact if a certain force is achieved. The installation of an aftermarket bumper doesn't change the amount of force required for the airbag to inflate, but it does potentially effect how that force is transmitted through the vehicle. This is where the crumple zones come into play.
A crumple zone absorbs the impact of a collision which reduces the impact on passengers and ultimately the amount of force translated to the airbag sensor. If you eliminate the crumple zone, you put more force into the vehicle at point of impact and you would on paper be more likely to trigger the airbag in the event of a collision of less force then with the crumple zone in place.
As for the stock 96 - 04 Tacoma front bumper, there is a crumple area on the bumper. It just looks like wavy steel. I attached a pic of the bumper without the plastic cover below. The ARB bumper replaces all of that and adds a large crush can which absorbs large impacts. I thought I had a picture, but for some reason I can't find it.
So the bottom line is airbags still work with aftermarket bumpers, however they make work differently. But companies like ARB work very hard to ensure their specific designs work as close to stock as possible.
Hope that info helps!
Pete
