Changing movie genre in AppleTV (4th Generation)?
Edit the genres in iTunes.  On the ATV, access the movies through Home Sharing, NOT through the Movies app.  Using the Movies app will show you movies you've purchased, but with all of the original data from Apple.  Using Home Sharing (the "Computers" app), you'll see the movies and genres stored on your local computer.

There hasn't been sync'ing since ATV1, I think...