They also refuse microlights, which made the bracket of aircraft they allow there a bit puzzling to me.
They do not refuse 'microlights', only flexwings. There are at least a dozen microlights based there and even a microlight school.
Some types may be banned because they are noisy and the owners do not want to give neighbours that oppose the airfield reason to complain.
Any accident that gets into the papers will give those same neighbours plenty of ammunition to call for closure or restrictions. Better to ensure that visitors do not spoil it for resident pilots.