Many people say that it's fine to use a standard household (cheap/dumb) 12V 4A battery charger to charge a car battery while it is still connected to the car. Others say that it's safer to disconnect the negative battery terminal and charge like that. Some quote car manuals which say you can charge in-situ it as long as your battery charger can't put out more than 7A (though I suspect that this may be a specific recommendation for those cars). Yet others say charging in-situ is fine for a healthy battery, but dangerous to the car electronics if the battery is dead or deeply discharged. Some also say that charging in-situ can 'spike' the electronics of a modern car, while others say modern electronics are more robust and there is more danger from the uninitiated dis/reconnecting a battery incorrectly.
I know from electrical engineering that no matter what the battery charger does, the voltage across the battery will ultimately be determined by it's internal resistance. I know that dead or deeply discharged batteries can have a very high resistance, and that as the battery gets fully charged the resistance rises, so some of the above statements seem likely. What I don't know is if the voltage across the battery would ever get high enough to damage other devices still connected to the car battery such as the ECU or devices plugged into an un-switched cigarette lighter.
It seems generally accepted that C/20 charging shouldn't cause long term damage to a lead acid battery, so an 80Ah battery should never be in danger from a 4A charger (This could be where the 7A max recommendation came from if the car had a 140Ah battery, or they though C/10 on a 70Ah battery was fine), however this appears to depend on whether the charger fixes the voltage and lets the current change according to the battery charge state, or whether the charger runs with a constant current and varies the voltage.
So, under what conditions, if any, should I consider it safe to charge a car battery in-situ, without disconnecting it from the car?