It is said that what comes out of an e-cig is water vapor. It might be water vapor because of some chemical reaction, I wouldn't know.(I'm sure someone with more chemistry knowledge will chime in) It could be that we say water vapor because no one would know what propylene glycol vapor is and panic, thinking it is some sort of horrid chemical.
Propylene glycol is a commonly used chemical. Look in your spice rack (imitation vanilla and other things) your medicine chest, your make up case, your diaper bag, and you'll find products with PG in them. The other "chemical used to make e-cig vapor is vegetable glycerine. You'll find that in your cookies and cupcakes.
PG has antibacterial/ antiviral/ germicidal properties. The air is actually cleaner with PG in it! They did some experiments many years ago with it. In one the had mice and another they had monkeys living for in a enclosed cage filled with PG vapor. The animals lived a long time, were fat and healthy and did not get sick. The scientists came to the conclusion that it would be beneficial for public health if PG vapor were pumped into places where groups of people pass germs around - like schools, large offices, shopping malls, etc. They didn't do it, probably for political reasons, but the the results were there that it would work.
Now I am not a fan of animal experimentation or government and science doing things "for the greater good." But we do now have this information, and it is useful for us. I would also say, always err on the side of caution when it comes to your pets, both for their safety and your peace of mind. Science would say it is safe to vape around your parrot, but you'll have to let your own conscience decide.
Be well,
~A