If it's an outboard and a remote fuel tank there is no problem. If it's an integral tank you have to be careful no fuel is spilled that could end up near a spark plug. Just remember it's the fumes that is where the danger is.
If it's a diesel does not matter anytime. When you crack the injectors with the engine running it is perfectly safe!
Lets be more specific..
If its PETROL and the tank is ON the motor
DO NOT REFUEL WHILE ITS RUNNING. 
Before refuelling also let the engine cool down!
I fuel up my outboard external tank while running. .cant think of how it could be dangerous. I dont smoke or have candles in cockpit
On Saturday afternoon at 1pm we left Bundeena on my Southern Cross 23 heading for my new mooring in Lavender Bay.
The strong winds on the nose made for heavy going and we were relieved and disappointed to have to stop in Botany Bay.
I dropped off my crew and picked up a well protected mooring at La Parouse.
As the forecast was for stronger winds today I posted this topic.
I left an hour before dawn as there was a full moon and I was keen to make Sydney harbour before the strong winds hit again.
It truly is a beatifiul sight to be at sea at sunrise.
As it turned out the weather conditions improved and I sailed into Sydney harbour three and a half hours later.
That to was great as I was passed at the heads by two racing yachts finishing an overnight race.
I motor sailed most of the way using my mariner 8 hp and was very surprised to find I had used less than ten litres of fuel.
It's hard to beat being on Sydney harbour on a Sunday morning on a perfect day.
Thanks again for the response to my topic.
