What is the ruling on turning on the television for a person who is predominantly assumed will use it for unlawful content, or giving them the remote control with the same assumption, and does sin result from that?

If it is highly probable that turning on the television will lead to watching something displeasing to Allah, then it is not permissible to turn it on nor to assist in doing so, for the Prophet, peace and blessings be upon him, said: "There is no obedience in disobedience to Allah; obedience is only in what is good." One should politely excuse oneself, especially to the father. However, if you do not know the purpose and it is not highly probable that he intends something forbidden, then there is no harm in turning it on, and the sin of watching something forbidden falls upon him, not upon you.