MacBook Pro to AirPlay Display

EXACTLY what do you mean when you say "AirPlay display" ??

Movies rented from AppleTV are copy-protected. They AirPlay on genuine Apple hardware devices, ONLY.

Consider connecting an HDMI cable to watch your movie. It will be far sharper and have better sound sync.

I identifying what you mean by "AirPlay device" is important to this discussion.

I have an older Sony Bravia TV that has Android installed. It is not a genuine Airplay device in that it is not made by Apple. There is software I could add that would allow the TV to mirror my phone and similar lightweight AirPlay activities. But watching a movie provided by Apple would be impossible because of copy-protection.

¿what model-year MacBook Pro?

I suggest you get a Mini DisplayPort-to-HDMI adapter and connect directly to your TV set HDMI input.