Am I obligated to encrypt the undesirable channels requested by my family, and would I be sinful for leaving them unencrypted?

If others are unable to prevent the forbidden channels, then it is obligatory for you to prevent them, provided that no greater harm results from it. This is based on the Prophet's (peace be upon him) saying: “Whoever among you sees an evil, let him change it with his hand; if he cannot, then with his tongue; if he cannot, then with his heart—and that is the weakest of faith.” It may become obligatory to change the evil if no one else is aware of it or is able to remove it except for him.