Every group has its factions. The "conservative" wing of US politics has seemed especially schizophrenic since the rise of the Tea Party, actively disrupting the coherence of GOP policymaking. Of course, this isn't helped by the entrenched two-party system, which lumps disparate elements together.
This is a good piece on the inconsistencies and tensions within the Republican party, and touches on the recent conservative in-fighting with regards to police power. I'd quote this entire article...
However, Rubin is right about stark differences between libertarians and many more conventionally conservative Republicans—there is a significant and perhaps even irreconcilable philosophical contradiction developing on the right.
But it is not between libertarians and conservatives. If looking for the most accurate and useful term to analyze this conservative dilemma, the opposite of libertarianism is not conservatism, but authoritarianism, and the current tension is between libertarians and authoritarians.
Libertarians distrust government. So have generations of conservatives. Conservatives have also long trusted and admired certain types of government—the military, the police, the Pentagon, the Central Intelligence Agency, National Security Agency—believing these bodies represent law, order, and safety.
Recently, ascendant libertarian Republicans have extended their skepticism of government to state agencies that the right is accustomed to giving the benefit of the doubt.