The EWG has released their Toxic Cleaners Hall of Fame list, which I thought worth posting here. I suppose to some it can seem as though you should not use anything around your parrot, but really, you should just not use anything that is toxic to both of you. And yes, that does still leave an awful lot you can use!
Go HERE for the list, with info on a variety of cleaners, laundry detergents, and air fresheners.