I'm defining "Western civilization" as "classical liberalism based on a system of Enlightenment moral ethics thereby government power is strictly limited under the objective rule of law". Or what you might call a weak form of libertarianism. As contrasted to actual "Libertarian Parties" with a Capital "L", which are a subset of the general group.
So, right-wing conservatism, summed up as "we need a gigantic Big Brother state to crush the enemies of religious virtue and social order such that we can maintain traditional authority structures as God intended" and "our nation-state must become a glorious Empire due to the superiority of our ethnicity and faith" would be the intellectual opposite of that logically. Authoritarian nationalism being the soul and spirit of modern conservatism. Which is the 180 degree opposite flip-side of libertarianism and the idea that "the best government governs least".
Western Civilization would be summed up by Dwight Eisenhour, George Bush Senior, Winston Churchill, Konrad Adenauer, and the like.
Right-wing conservatism would be summed up by Benito Mussolini, Jair Bolsonaro, Donald Trump, Vladimir Putin, Jean-Marie Le Pen, and such.
There's a linguistic issue in the U.S. because libertarianism and conservatism are intellectual opposites in the dictionary form, but American nationalists and other advocates for big government in the U.S. tend to call themselves "libertarian". Also, in America anarcho-capitalists and neo-Nazi types are both called "of the political right". I'm inclined to just think of that as lying and not take it seriously.
Actual libertarians don't support fighting the legalization of drugs, imposing rules against free speech, banning certain types of food for being too unhealthy, imposing discrimination against LGBT people, deepening U.S. debt and deficit spending, and other doctrines that U.S. conservatives fight tooth and nail for fanatically.