If it were *my* house and bird, I would probably put up a baby gate to form a "safe distance" perimeter around the parrots cage with a large "I BITE. PLEASE DO NOT TOUCH" sign, in addition to stressing the importance to the realtor that people not approach them. Even if your birds are the most loving sweethearts of all time, no one will be keen to approach them when they see the beaks and a big sign that says they bite

After all, you're selling the house, not the birds! Not to mention, some people practically need to be smacked in the head with a brick to understand a basic concept like "don't pester the parrot", so doing a little more than probably necessary is better than hoping an idiot doesn't view the house IMO.
When we lived in our old apartment, there were a few times the maintenance man had to come while both of us were at work and I was so scared he would try to be friendly with Kiwi and stick a finger in the cage (and get it ripped off). I would always put a big sign that said "My beak can remove fingers. Please do not touch!"

Not appropriate wording for a house showing, but even when one of us were home, the guy made a wide berth around Kiwi's cage lol. Always better safe than sorry these days. Idiots are allowed to sue for their own stupidity, at you and your birds expense.