Gamekeepers are, quite rightly, very protective of their birds, especially at this time of the year, and are keen to minimise disturbance.
However, a zero policy on shooting is going too far.
As a keeper himself, he must be shooting to keep down pests. Shooting around pheasant pens and feeding stations is obviously out of order, but the odd shot from a rifle will cause no lasting damage to the birds.
If you were regularly shooting clays or sighting-in a rifle near feeders then the birds might indeed become jittery, though it is amazing how repetitive noise is often ignored by wildlife if it proves to be non-threatening.
You have even more reason to be upset if you are using a sound moderator.
A .22 rifle or air rifle with a moderator will cause minimal disturbance, as will a shot at a deer or fox.
The shot may engage the birds? attention but, if not followed up by a second shot, they will soon go back to feeding or resting.
Try talking to your keeper again and explain that you will co-operate with him but feel that a complete embargo is uncalled for.