There is a lot of info on this post from people that are over thinking the issue. Put the charger on a separate circuit breaker, the black wire is usually piggy backed onto the fridge circuit. If you have the infamous WFCO ther manual even shows you how to do this. Yes it is a fully manual affair, when using inverter switch off charging breaker, plug in inverter. If using gennie to charge batteries, you unplug from inverter to connect to gennie, flip charger circuit back on.
I been doing it thus way for 10 years on my TC. On our fiver we do it the same way except I use a stand alone charger and the integrated charger circuig is left off all the time and is there for emergency situation. This method is going o it's third year now, no fires, no dead batteries, no near death experiences.