This is a charade - multiple parts are joined together in sequence to build the final answer.
Break this into three parts: 'Following' gives you a single letter, 'rubdown with oil' refers to a ceremonial religious practice, and 'everything' is a short word meaning 'all' with one letter removed (indicated by 'not quite').
Answer: FUNCTIONAL | F (following) + UNCTION (ceremonial application of oil) + AL (all with one L removed, meaning 'not quite')