Wasn't there a pretty long airbag thread on SOR last year?
Here's my question: the airbag sensor(s) are not connected to the bumper and are really inertia devices, no? So what changes with the ARB is that there is less 'give' when you hit an object. We call them 'crumple zones' now, where in this case the bumper deforms to absorb a portion of the impact.
Now a fair number of you have removed your front bumper to put something else on. That bumper will probably 'absorb' it's max. in up to a 15 mph crash against an imovable. Anything above 5 is going to start damaging a bunch of other stuff as well (which makes your grill, radiator, hood, engine, etc. into a 'crumple zone') or the frame rails are going to hit said immovable object and you stop real quick.
The ARB and others bolt right on up to those frame rails so when you hit the immovable object, the 'crumple zone' of sorts that is the front of your truck no longer exists.
Now I can't remember at what speed impact with an immovable object the airbags are supposed to deploy but lets say it's 15mph (it doesn't really matter too much here).
<15mph impact with immovable:
Stock - fair amount of expensive damage, no airbag deployment, minimal impact (relatively) on occupants
ARB - negligable damage to bull bar, poss. airbag deployment, moderate impact on occupants (less car absorbing the kinetic energy of the vehicle through deformation over time, more sudden and powerful impact on occupants)
>15mph impact with immovable:
Stock - significant damage to front, airbag deployment, moderate impact on occupants
ARB - moderate damage to front (as long as frame is not bent of course / high-speed), airbag deployment, significant impact on occupants.
It's the same reason that although the old American cars can really come out of a crash with something newer looking a lot better and with a lot less damage, the occupants in the newer car have fewer injuries (by a surprisingly large margin). When you put a bull-bar on the front, you reduce the amount of impact the car itself will absorb which loosely (but definately) translates into a greater 'impact' on the passengers.
The purpose then of the bull bar is to protect damage to your vehicle at the expense of passenger safety IN A CRASH WITH AN IMMOVABLE OBJECT.
Where it gets even more gray is when you hit another car (same mass as LC). Two crumpling masses are better than one but if your bull-bar hits their crumple-zone then their vehicle has to absorb twice the energy (this is obviuosly over-simplistic but it gives a decent idea). If you hit something with significantly less mass than the LC (deer or Jeep

for example) then the bull-bar prevents damage to your vehicle with most damage being done to Bambi's mom and not your truck.
Geez, if your still awake...
The net result of all this is that the bull-bar may make the airbags go off at a slower speed impact than stock HOWEVER (and this is a BIG however) the airbags will still go off at the same 'impact point' or change in inertia as they did before! The airbag isn't related to the speed directly, think of it as being related to the amount of impact on the occupants! With the bull-bar, the occupants are more affected and when they are, the air-bag will go off as it would with stock.
It's not some touchy little magic box that's going to go off every time you parallel park (if you park like I do that is) but bull-bar or not, when the sensor reaches a threshold where the airbags shold be deployed for passanger safety, they will.
Anyway, I don't know if that makes sense to anyone but I leave 'em on with my ARB. If I hit something hard enough that they should go off, I want them to go off (trail or no trail - just be sure you know how to get the truck rolling again!)...