I've been called "bird lady" before, mostly by kids. Can't remember anytime where "crazy" has been put before those two words to my face, but I imagine it most likely might have happened in a conversation between two people, since I do know a few of my friends/acquaintances do think owning parrots is something someone crazy would do.
When people think that with 6 I have a lot....I just tell them I know people with twice to five times as many and that shuts them up...