You're trying to talk about Republicans as having a single coherent philosophy, which is just not so. Same with the Democrats. Because of our voting system, there are only ever two viable parties, and so both parties have to be broad coalitions. The Republican party is a broad coalition of social and religious conservatives, libertarians, international realists, and neoconservatives.

Libertarian, Green, Reform, and other third parties are nice side shows, and good ways to get alternate ideas heard and stimulate conversation, but if you're serious about actually winning and exercising political power, you need to work inside one of the two big tents.