The battery isolator probably disconnects the house battery on the trailer. If it's OFF, plugging into shore power shouldn't be charging the battery. If you leave it ON and continuously plugged in, you might overcharge the battery, or at least run it dry. So, after initially charging the battery or recharging it after a trip, I'd turn it OFF.
Leaving it ON while plugged in at a campground for a few days shouldn't be an issue. Similarly for short periods of generator use.
You might want to check if there's a separate battery charger switch.