When I changed batteries recently I made sure I had the radio code.
Then I took the old battery out and fitted the new one.
OK so far.
But on opening the car door the alarm went off. It took me a minute the find the keys, blip the button twice to lock & unlock the car and then all was well.
'98 D 800 van
A diode bridge or bridge rectifier is protection against reverse polarity on a battery charger, for example. (A diode only lets current flow in one direction.)
This, like most sensitive electronics fitted to modern vehicles, could possibly be damaged by a high current surge, but not by voltage as you are never supplying more than 12v (or 13-14v from a charger) in to the battery.
In years gone by cars used a DC generator to charge the battery, but their output was dependant on rpm. At tickover less output current was produced.
(Remember dynamo lights on bicycles; the faster you pedalled, the brighter the lights.)
Modern alternators use voltage regulators to supply a constant voltage and more recent vehicles now use the ECU instead.
A diode bridge on an alternator converts the AC current to DC and they are about 70amps on a modern car.
As most battery chargers provide a quarter of that current, I cannot see how charging a battery when connected should cause a problem.
If you want to be on the safe side, disconnect one lead when charging. Doesn't matter which one, as you are 'breaking' the circuit.