YouTube has a lot of content, not all of which is acceptable for kids. Actually, a lot of it isn't acceptable for grown ups either, but that's beside the point. The YouTube Kids app was launched last year to aggregate kid-friendly videos, but it didn't support YouTube Red. Now, it does support YouTube Red, which we predicted in an APK Teardown earlier this year.
When signed into YouTube Kids with a YouTube Red account, you get offline saving, background play, and no ads. The ad-free experience is particularly important as the video itself might be fine for kids, but sometimes the ads weren't. YouTube Red costs $10 per month and comes with Play Music streaming. The opposite also works—subscribe to Play Music and you get YouTube Red.
YouTube says it's also working on adding features to the Kids app that will allow more customization of content. Considering how long it took to add YouTube Red, I wouldn't hold your breath on that.