Older chargers that do not have blocking diodes (such as some of the cheap automobile variety) - yes, probably not a good idea to have shore power attached. However, if you have a newer system in place - you will never have a problem.
Here is why:
When the internal engine is running and the alternator is running correctly - the alternator has Voltage sensor just as the AC chargers do. There will be an initial switch on and switch off between the units but the Alternator will usually win the battle for charging the missing cranking amps, as the AC Charger is more sensitive and cuts off more quickly when sensing the voltage is higher than the float / max charge level (which the alternator puts on the line
). The alternator will be a bit slower as it is sensing the pull it using to crank the engine but the AC charger will immediately sense it and shut off for protection. However, if the battery is severely drained - it is possible for both to charge at the same time - but the AC charger will go into trickle mode.
However, older systems - older Charge Units - are not necessarily as sensitive / smart with the charging but they too usually should have no problem being on when the engine is running as they are all designed to shut off when max Voltage is detected.
Causes of fires etc, are usually improper grounding or not using the appropriate gauge of wiring on either of the systems causing overheating and eventually fire. Or placement of fuel
tanks too close to the engine without the space being properly ventilated before being engine is started. Most accelerated corrosions or quickly dying alternators
are usually caused by fuel
vapor or oil coming in contact with with the windings in the Alternator. These deposits in the end cause the alternator to arc and spark internally (and if not fire - will kill the alternator rather quickly).
Considering that both RV and Marine utilize similar techniques (actually the same - except the chargers for boats are 'marinized', for example the same Xantrax charger I have on my boat is the same as the on on my Airstream) . I would of blown my truck's alternators
a long time ago by having AC power hook-up to the RV at the same time the truck is running and connected to the RV (as the RV's battery banks can be charged from the trucks trailer connection).
While it probably is best to disconnect - as it puts one in the habit of not pulling out without dragging the shore power cable from the dock... it is very unlikely with the proper system in place - that electrical issues would result with having shore power and the engine running less a failed component, poor ventilation if fuel
vapor is present in the area of the engine (alternator), or improper wiring.
Just my 2 pesos...