Well, the Fair Housing Laws say you cannot discriminate.

And,

Zillow and Private investors are coming in and offering above asking prices (way above) to outbid any regular people in my area. Who is going to turn that down?

Also, any normal person can come in and buy your house and immediately remarket it to the Zillow investor cabal and reap the profit you would have made if you had sold directly.

It's a dilemma.