It may be the Child Filter
If the Child Filter is turned on for the user that the device is connected to, all content not flagged as child safe by YouTube will be blocked.
We've received feedback from our users requesting a bit more fidelity in selecting the filtering level, and we are currently developing a solution.
For those with younger kids, YouTube has a Kid Specific app called YouTube Kids. There is no URL to access it like the YouTube site, but instead, there are Apps for iOS and Android. They also over resources to assist parents as well.