Some bumpers will change how the front of the vehicle behaves in an accident and will effect airbag operation. To what extent is another question, but generally replacing the factory bumper and it's energy absorbing components with a solid metal mounting system/frame will decrease the trigger speed at which airbags deploy. This means your airbags might go off when normally they wouldn't. Luckily it doesn't mean they won't go off when you really need them.
It's all about deceleration forces. With crumple zones, deformable elements and energy absorbing parts, the deceleration rate is slower, meaning you might go from 45mph to 0mph in 0.5 seconds (example only). With an aftermarket bumper and it's stronger parts that don't deform as easily you might go from 45 to 0 in .3 seconds. That's measurably quicker and means everything is experience higher forces.
Most small aftermarket companies do not have the engineering resources and money needed to design, test and manufacture systems that do not change the way airbags work. ARB on the other hand, are a very big company and they did the design and testing on mounting brackets that performed in a way so impact and deceleration forces did not change airbag performance. They actually crash tested a brand new 100 series Landcruiser during the design of their system.
I'm don't think the difference is a big issue, just something to be aware of. There was one guy with a 3rd gen who hit a brick mail box with a Shrockworks (iirc) bumper and the airbags went off. That surprised everyone, but without a proper study, we don't really know what would have happened otherwise.