I don't see why it would be illegal to have an exhaust fan running 24/7, but you could call your local building inspector to ask them. Obviously the answer to that legal question depends entirely on your local laws and building codes, so there is no blanket answer.
As for "green", which is a very vague term, I agree it seems a little wasteful but it depends on how much electricity the fans and lights are using and how much of your conditioned air is being vented outside.
To calculate how much an appliance is going to cost to run, you can use this formula:
Monthly cost = (Appliance watts) X (hours per day) X (days per month) X (price of electricity in $/kWh) / (1000 watts / kW)
So in my area to run a single 30 watt exhaust fan 24/7 for a month would be:
(30 watts) X (24 hrs) X (30 days) X ($0.20 /kWh) / (1000) = $4.30
If these fans are running all the time they may be a lower wattage, or you may have lower electricity rates than I do, so should do your best to find out what your actual numbers are if you're concerned about the electricity cost.
If you have the heat or AC on, there's also a cost associated with losing the conditioned air. Any air that vents out of the house will be replaced by outside air that is drawn into the house through cracks, and will add additional load to your furnace or AC. The numbers are harder to calculate, though.