Most RCDs have a circuit breaker incorporated (so they are a RCCB) but the marina usually has a seperate lower value circuit breaker installed.
If the RCD trips rather than the seperate circuit breaker it is unlikely to be an over current problem. Rather an imbalance between the Active and Neutral feeds. This is what the RCD responds to.
The aim is to prevent electrocution. An imbalance between the current in the active and neutral wires means some current could be traveling through a human. The RCD is designed to trip before the level where this current is likely to be fatal.
The problem is this current is very small. Many perfectly normal pieces of AC equipment
leak a little bit of current even though they are functioning normally. As equipment
ages the level of leakage increases, especially with dirt and carbon accumulation. Thus the RCD can trip when connected to equipment that appears to be working normally. Of course the marina RCD can also be faulty, but if you are getting this problem in several locations it is likely the leakage is something on the boat.
Sometimes it is a small amount of leakage through lots of different equipment, but with your sort of problem it is generally one piece that is causing most of the nuisance tripping. The first step is to try and identify where the leak is occurring.
If the RCD is tripping even occasionally with just the battery charger connected and all the other boat circuit breakers off it suggests the problem could be with:
The shore power cord
The shore power socket
The wiring/connection circuit breakers etc between the shore power and the battery charger.
The battery charger itself.
The shore power cord itself, or the plugs and sockets are by far the most likely cause of this problem (even though they seem to be working normally). So the first step is to borrow a different shore power cord and also try cleaning
all the shore power sockets etc.
If this does not fix the problem clean all the AC connections and finally the battery charger itself.
A small amount of salt
grime can carry enough current to cause a trip.