nothing [adjective phrase] about X is a colloquialism. It is a way of saying that the modifier does not apply to X.
The restaurant had a glass-enclosed veranda with the shades pulled down because of the sun. There was nothing al fresco about it.
The film was very tame. There was nothing "X-rated" about it.
The speaker in your example is tweaking the pattern by using the noun-phrase "family values" in place of an adjectival modifier. It is elliptical:
Acting with a monkey does not promote so-called "family values".
The adjectival modifier "[promoting] family values" is not applicable.