That’s why we typically plot political views on a two-axis chart. The libertarian-authoritarian axis and the left-right axis. The two are entirely different in nature and it is entirely possible to be a leftist libertarian or a rightist one. Your position on the libertarian axis is determined by how much you love the use of government power. Libertarians seek to eliminate it as much as possible, authoritarians seek a totalitarian state that runs your life in every way. The left-right axis is divided on the question of equality. The left holds equality to be the highest virtue, to be achieved by all means possible. The right believes that each individual is unique and that to try to make everyone equal in any way is immoral. Additionally, there may be a conservative-liberal split, mostly based on religious beliefs.
American conservatism isn’t about authoritarianism at all, it is about a functioning, decent, God oriented, family friendly culture that leads to conservative voters.
Libertarianism/liberalism breeds, creates, and imports, lefty voters which leads to authoritarian government, the last 50 years proves that.
Conservatism is one the verge of being destroyed by the libertarian/lefty double team as even the rinos in the GOP embrace the libertarian agenda on social liberalism.