I know this is an old thread, but I just wanted to put this here because it is the first result in Google to come up when searching "airplay keeps popping up on Roku TV".
There's a setting under AirPlay to disable it entirely. I don't have any Apple products, so this doesn't matter to me if this is shut off. I live in transitional housing so there might be other people on my network doing it by accident. Hopefully this solves my problem. Airplay tended to keep popping up when I opened the Roku remote app on my Galaxy Watch 4, and it didn't when I tested it, so it should solve the issue.
