If I follow your logic, for the sake of people with a peanut (or any severe) allergy, all flatware at Disney should be discarded instead of washed - whether plastic or metal.
Plenty of other posts on this Thread have pointed out that BoG turns into a table service restaurant for dinner - so it likely has a dishwasher to sanitize. Also, have you seen maps of Disney QS - many (if not most) are attached to table service establishments behind the scenes - where a dishwasher would be located.
Further still, you are ignoring how plastic utensils are obtained - anyone can touch the lever that dispenses plastic utensils, even people who might have been in contact with peanuts. How about the trays - are they sanitized before being loaded with paper plates and plastic utensils? If so, even QS have dishwashers to sanitize; if not, then your argument falls-flat again.
And while I gave an example about plastic versus metal utensils, you seemingly ignored all the other places where Disney simply fails to be green, like using more expensive paper straws in Animal Kingdom, but less expensive plastic ones every place else. And anyone can touch these dispensers - even people who have been in contact with peanuts.
I'll state it again, unequivocally - Disney is not as 'green' as they could be - and it has nothing to do with preventing the spread of allergens.