Nope OEM immobilizers are not safe. Anybody with a FSM can pretty much bypass an OEM immobilizer and it has been done and continues to happen.
If they don't use the FSM then they will walk around with the bypass devices, replacement ECUs with cracked keys, etc... However those are more the professional type and chances are if they really want it, they will take it.
Locally you don't hear about it as much but it happens in other places of the world much more frequently. Down here our problem is gun point theft of newer vehicles and well either gun point or stand still theft of older ones.