Yeah keeping both open is normal but what if both sides are leveling? Or gathering/trashing mobs?
Personally I tend to do not bot both at once but to be honest I would be very surprised if Blizzard North and Blizzard South would communicate togheter to find such behaviors.
Still it is weird from others players view, especially your Real ID friends that see both operate on their friend list...
I feel it is not safe especially with friends around...