Is it permissible for a Muslim woman to marry a young Muslim man whose parents are not Muslim?

If a young man is satisfactory in his religion and character, it is permissible for a girl to marry him, based on the saying of the Prophet, peace and blessings be upon him: "If someone whose religion and character you approve comes to you, then marry him. If you do not do so, there will be tribulation on earth and great corruption." The fact that the young man's family are not Muslims does not prevent marriage to him.