All doors closed with engines running (supposedly JAR-conforming FOM).
Excepctions only if engine must be kept running, e.g. when APU U/S and no airstarter available (tail mounted engines only, so no danger of ingesting a baggage handler :-)
Handling of exceptions has to be coordinated between ground handling and captain, so I'd think it would at least require a headset connection.
In practice, they sometimes ask to open and usually get permission, even if no "special case" exist. On the props it's not really a problem with the baggage door far behind the wing and the engines not producing any thrust. As the guys around the airplane have to know how not to walk into running props anyway, I don't see a special danger in letting the re-load after engine start.