Is requiring and blatantly stating in the handbook that women are to wear makeup sexual discrimination?

Interesting question.  The answer is probably not if the employer can show that it does not create an unequal burden based on gender and is actually related to the function and purposes of the job. The situation you describe was actually the subject of a high profile case against Harrah's Casino.  See Jespersen v. Harrah's Casino.  In that case, the Plaintiff challenged Harrah's "personal best" policy which included a requirement that women wear makeup.  The District Court found that the policy did not create an unequal burden on female employees since male employees were required to be well-groomed and keep their hair short.  Although it seems like a stretch of logic to compare the grooming policy as applied to men, and as applied to women at Harrah's, the Court found that they imposed similar burdens regardless of gender. The Ninth Circuit Court of Appeals agreed in part, but stated that if the policy was motivated by sex/gender stereotyping, it could be found to be discriminatory.