That works...but do they have to be mutually exclusive? A lot of neoconservatives abandoned, at least temporarily, the Republican Party after the Bush debacle (people like Francis Fukuyama) but aren't there those who identify as neocons but are anti-gay, anti-Islam, pro-personhood and anti-drug reform?
In theory, they are mutually exclusive, since neoliberals are often socially apathetic. In practice; however, a neocon could get bent about a particular social issue, and adopt new right policy, without changing his neoliberal economic sentiments. His dominant political orientation would be difficult to discern. New Right hater? or Neocon with an axe to grind over a particular domestic social issue?