Yes, he is somewhat of a combination of the two (libertarianism and traditional-values conservatism). That’s usually what people are, of either stripe: a combination.
Ideologically, however, the two do not mix. It’s like socialism and free-marked capitalism. We have a mixture in the United States, but there is an inherent conflict between the two, and the complete domination of either one would eliminate the other.
Then you do believe that:
Libertarians = anarchy
... and ...
traditional-values conservatives = fascist theocracy?
Social conservatism and libertarianism are not intrinsically incompatible. There are health and financial consequences of most immoral behaviors - gluttony, alcoholism, sexual promiscuity, teen/unmarried pregnancy, and drug use being obvious examples. With no social safety net to bail you out financially and no government to cover your medical bills, there is much more of an incentive to lead a moral life than under a nanny state.
Now, it is true that libertarianism is incompatible with a system where the government mandates individuals to live a moral life. Some will choose to live immoral lives regardless - the difference is that you won't have to subsidize that kind of behavior.