Will disconnecting the negative battery lead disable all airbags? I need to remove some bumper brackets that connect to the chassis.
If you're out banging on the bumper brackets and set the airbags off, you won't be getting blown up. Maybe that friend waiting inside the car. Yes, car off and 12 volt battery disconnected will suppress all airbag activity, provided you wait at least the specified time after disconnecting for stored charge to bleed off. I forget exactly what the time is in the repair manual, some matter of minutes, I think.
As @bisco kindly suggests, the Repair Manual (more info) explains the required precautions for the supplemental restraint system (SRS). See the topic General: Introduction: Repair Instruction: Precaution, under the heading “For Vehicles Equipped with SRS Airbag and Seat Belt Pretensioner,” where Toyota writes: (2) Work must be started at least 90 seconds after the power switch is turned off and after the cable is disconnected from the negative (-) battery terminal. The SRS is equipped with a back-up power source. If work is started within 90 seconds after turning the power switch off and disconnecting the cable from the negative (-) battery terminal, the SRS may deploy. When the cable is disconnected from the negative (-) battery terminal, the clock and audio system memory will be cleared. Before starting work, make a note of the settings of each memory system. When work is finished, reset the clock and audio system as before. CAUTION: Never use a back-up power source (battery or other) to avoid clearing the system memory. The back-up power source may inadvertently power the SRS and cause it to deploy. Toyota also writes: Before using an electric welder anywhere on the vehicle, disconnect the center airbag sensor assembly connectors. These connectors contain shorting springs. This feature reduces the possibility of the airbag deploying due to current entering the squib wiring. If you disconnect this connector, be sure to follow these additional points: (2) The connectors to the center airbag sensor assembly should be connected or disconnected with the sensor installed to the vehicle. If the connectors are connected or disconnected while the center airbag sensor assembly is not installed, the SRS may activate. (3) Work must be started at least 90 seconds after the power switch is turned off and the cable is disconnected from the negative (-) battery terminal, even if only loosening the bolts of the center airbag sensor assembly. When removing, installing, or handling pyrotechnic SRS parts (the steering pad, airbag assemblies, and front seat outer belt assemblies), further precautions apply, all explained in the Repair Manual.