But there are allergies to bird feathers, for example in pigeon breeders. Can the same happen with bed-feathers, too?

 
This form of allergy occurs when substances, which trigger the allergic symptoms, enter the human body via the airway system.
It is an allergy, however, which is virtually unknown in the context of the bed-feather allergen.

A survey on bed-feather (keratin) allergy by Prof. Dr. med. Dietrich Hof­mann from the Clinical Center of the Johann Wolfgang Goethe University, Center for Pediatrics led to the following results:
 
This form of allergy – the type III allergy, which can basically be triggered by bird feathers, for example by feathers from pigeons and budgerigars, “is, however, virtually unknown in the context of the bed-feather allergen, since long-lasting exposure to high concentrations of the allergen is the precondition for the manifestation of this group of diseases (allergic alveolitis). At the most, such a scenario could become reality for somebody, who worked, say, in the bed-feather industry and would be in close contact with the filling materials themselves.“
Quelle
Verband der Deutschen Daunen- und Federnindustrie e.V.