bunjywunjy answered:

not at all! as we can tell from his general behavior and repeated comments about how delicious birdseed is, Big Bird is a megafauna herbivore and a keystone of the Sesame Street ecosystem!

Big Bird is too large to be challenged by the predatory muppets, so he can browse where he pleases, and in doing so he opens up spaces and opportunities for the smaller muppets, both predatory and non-predatory alike!