Please keep in mind that onions are toxic to dogs and cats and can cause blood problems. I would not give any kind of onion or onion flavored foods to our pets - even if they would eat them.
I know that onions are dangerous for pets, but I honestly never made the connection to Funyuns... Although, they are to onions what Cheetos are to cheese... probably no real onions involved. Anyway, I will not be giving them to my girl any more!