If you have problems AirPlaying a HD (high definition) version of a movie purchased from iTunes, then the instructions below may be of some help [Assuming iTunes offers a SD (standard definition) version of the movie]. If you've already purchased the HD version, iTunes should allow you to download a SD version (if available) for no additional charge.
1)Delete HD version of movie if already downloaded
2)Go into itunes->store->movies or tv shows->very bottom of page choose "purchased" under "features" footer menu
3)Uncheck "download hd when available". It will then show all of your purchases that have a SD version you can download
4)Re-download SD version
Clicking the movie picture will take you to the sales page. Click the cloud icon
(Instructions courtesy of Erik Clark 2-14-19)