According to recent update to the official Netflix Help Center webpage, Airplay is no longer supported for use with Netflix due to “technical limitations.” AirPlay lets you share videos, photos, music, and more from Apple devices to your Apple TV, favorite speakers, and soon, popular smart TVs.
I find this a bit strange and questionable. My suspicious mind thinks that it a bit of retaliation for Apple’s plans to launch its own video streaming service, Apple TV+, this fall. But perhaps I’m just a conspiracy nut; we’ll see if Netflix gets those technical difficulties worked out soon.
Update: my theory may be wrong. Netflix issued this statement to MacRumors: "We want to make sure our members have a great Netflix experience on any device they use. With AirPlay support rolling out to third-party devices, there isn't a way for us to distinguish between devices (what is an Apple TV vs. what isn't) or certify these experiences. Therefore, we have decided to discontinue Netflix AirPlay support to ensure our standard of quality for viewing is being met. Members can continue to access Netflix on the built-in app across Apple TV and other devices."