When I was about 7-8 years old, my parents had a couple come for dinner. The man was some important business associate from my father's job. My brother and I were usually allowed to say hello and then we had to go to our rooms. We usually took our beloved Budgie, Mickey out of his cage to kiss him good night and then put him back in his cage. (the photo is of my brother Roger kissing our beloved and totally innocent, Mickey) Usually he behaved but that evening he decided to fly around the room. Turned out the woman guest was terrified of birds and started screaming as if she was being attacked by vampires. We tried to catch him but he decided to play and we were jumping around the furniture so it was a game for us too. Finally my father, who also loved him, reached up his hand caught our little aviator and put him back in his cage but the woman insisted that he put Micky where she couldn't see him as far away as possible so he came upstairs with us. The woman didn't relax for the rest of the evening and my mother was a very good cook!
When my double yellow-head Paco first came to live with me, I had a friend who was so bird phobic that she wouldn't come into my house. One day she asked me if I would help her get over her irrational fear of birds. She wanted to start out by coming into my house with Paco's cage covered. That went OK and gradually we went to her sitting in the house with Paco's cage uncovered, then with Paco on the cage, then with me handling Paco. Within a few weeks, she was actually handling Paco. Eventually, she gave Paco special invitations to come to dinner (If I brought her, I could have dinner too) and set a special place for Paco at the table. Paco loved her linguine. Phobia cured!
My third situation was on an airplane. I was moving to California and my grey, Bongo Marie, was in a carrier under the seat in front of me on the airplane. I was in an aisle seat and Bongo made a little chirpy noise and then started talking. With an alarmed expression on her face, the woman in the middle seat asked if there was a bird under my seat. Within a fraction of a second, she practically jumped over to me screaming to the flight attendant that she couldn't stay on the flight with a bird on the plane. The flight attendant managed to calm her down. I was agreeable and the attendant found Bongo and me a seat in the very back of the plane. I had to agree that I wouldn't let her out of the carrier. I did and explained that she couldn't fly anyway. Bongo ended up entertaining the folks in the back of the plane with her nonsense. The flight attendant was very nice and even brought me an extra treat from first class.
While some orniphobics may be able to tolerate a bird in the room, it would be very unusual for a person with a real bird phobic to even have a bird near them.