I observe that there is a category of individuals that call themselves Conservative* Libertarians. They explain this by supporting libertarian economic policies and conservative social policies.
Can this be consistent?
In theory, maybe they achieve this, but what about in real world? When it comes to decide about an issue, wouldn't they have to choose either to support conservative or libertarian policies? Wouldn't conservative viewpoint surpass their libertarian ideas (and the other way around)? If you think that their viewpoint is controversial, can you present me some real-world examples in which they would have to decide either to support conservative ideas or libertarian?
*By saying conservative, they do not mean the traditional meaning. For example, they support war on drugs, gay marriage prohibition, religious & national (i.e. flag burning) blashemy prohibition etc
Not that "conservativism" is even a consistent position nowadays, but certainly if they are for the war on drugs that is in direct contradiction to the libertarian view that people can do whatever they want as long as they harm no one else. So yes, they are in contradiction, but people have no problem holding contradictory viewpoints, due to compartmentalization.
Why anarchy fails
How do they consider themselves Libertarian?