If Mazda used an immobilizer system, yes. But if they did it like Honda and didn't use that then car car is just as vulnerable as any older car, like my Civic was. As time has gone on the "OBD2" systems in cars are hardly OBD2 anymore by virtue of how the electronic gizmos communicate with one another; systems these days are almost proprietary.
Take a new Mazda for example. The radio is an integral component in the starting of the engine. If somebody breaks into your car and steals your radio they've just gone through a lot of trouble for nothing, because not only will the radio not work until it has communicated with all the other computers in that individual car (the gauge cluster being another, besides the PCM and whatever else a company might use), but the engine won't start until the PCM has communicated with the radio, cluster, etc. They're all intertwined. You can't even take the radio from one 3 and put it in another without rooting through a diagnostic computer to reset codes and whatnot. In order to steal cars with systems like these you would literally need the diagnostic computer and software from the dealership, a technicians thorough knowledge of how to do this, and a contact on the other end of the tech line who will confirm your name, your dealership, authorize the procedure, and give you the codes required to complete it. Without those, stealing the car, much less stealing the radio, is impossible.
While my buddy's 2001 Miata had a chip in the key, the car could still be stolen by a crook persistent enough to fiddle with radio transponders. There's no particular date when car companies started going crazy with these Controller Area Network diagnostics, it's just something they started doing.
My truck computer runs the fuel injection and the OBD-I system, nothing else. I can run it without a radio, without a cluster, without a battery if I start it before disconnecting, anything.
