The context is Ameristanian politics & philosophy.
And it's in a non-debate section, the conflict inherent in the question notwithstanding.
Let's discuss it....especially among those who identify as conservative, libertarian,
&/or classically liberal (sometimes called Jeffersonian liberal).
(I identify as all but conservative.)
Some background worth reading (too detailed to excerpt meaningfully).
Classical liberalism - Wikipedia
Conservatism in the United States - Wikipedia
I see classical liberalism as closer to libertarianism in social & economic thought.
Note that both are not so rooted in religion. But conservatism is deeply rooted
in Christianity, & seek its influence in government.
If we're talking about the classical liberalism of our Founding Fathers, then
I guess it's hard to put into context, since America's Founders were, by definition, revolutionaries implementing a revolutionary form of government. There were no "conservatives," per se, except for those who still wanted to remain part of the British Empire.
Some of the early political disputes appeared to be more regional - not so much a matter of "liberal" vs. "conservative." The North favored industrialism and free (but mistreated and exploited) labor, while the South favored agrarianism and slavery. Both favored expansionism, so there were no real "peaceniks" to speak of.
The early Abolitionists might have been liberals of their time, although they were also devoutly religious, along with some genuine fanatics like John Brown.
I think the modern versions of "liberal" and "conservative" were mainly formulated and developed after the Civil War. I think that conservatives might look back on this era as a kind of "golden age" of Americana. That's when patriotism reached a peak. The opening of the West was considered a milestone, and that was also near and dear to Americans' hearts in later years, as Westerns became the most popular genre in film and TV. It was good for capitalism, too, as America's industrial machine was still young but had a lot of potential.
But liberals were also out there pointing out the many wrongs taking place. Despite the Civil War and the end of slavery, there were still abuses taking place in the South, as well as in the West with the Native Americans. Child labor and other horrific abuses continued in the factories. Railroad workers and miners were also getting more restless. The cities were rapidly growing, but turning into utter sewers with unhealthy, disease-ridden conditions that liberals and progressives decried.
There were also those on the liberal side who resisted and rebelled against some of the religious-based standards of morality that had been imposed upon them previously. People started believing in things like "free love," but the conservatives would have none of that.
Teddy Roosevelt was a progressive. He believed in environmentalism and anti-monopolism, much to the chagrin of his fellow Republicans who were more conservative. Woodrow Wilson also supported more progressive policies. Roosevelt was quite a war hawk in his later years as WW1 started up, and Wilson himself declared war in 1917. But there were quite a number of Americans who still wanted peace, and America's subsequent isolationism was largely credited to conservatives.
Conservatives took back power in the 1920s, which led us into the Depression, for which conservatives were blamed. FDR was more liberal and supported liberal policies, but he also supported war and a more internationalist policy which was initially opposed by the more conservative factions who tended towards isolationism. But then they inexplicably made a sudden switch and became even more zealous warmongers during the Cold War, while some liberals were starting to question it (although there was some division among Democrats at that point).
The conservatives also fought against civil rights, while liberals largely supported it.
They still seem to squabble over the idea of "free love," although it appears that liberals were the overwhelming victors in the sexual revolution. Then there was also the counter-culture and the "chic" factor of illegal drugs, which may have been underground, but still very much a part of the culture. So capitalism, on a certain base level, had a certain kind of appeal to the liberal free thinker who rebelled against the fuddy-duddy attitudes of religious conservatives.
This is where the libertarians come in, at least in the modern era. They strike me as those who were rebels in their youth, part of the counter-culture - sex, drugs, rock and roll. They like the idea of free love and so forth - and they want the liberty to do whatever they want, provided it doesn't violate other people's rights. In that sense, liberals aren't much different, except they believe in government social programs to help the poor and disadvantaged.
Conservatives also seem to carry a certain libertarian thread to their message, as they also claim to favor the same things in terms of civil liberties, property rights, free market, etc. Although they also have a lot of the religious conservative attitudes, as well as a good number of warmongers and ultra-patriots.
I think libertarians have borrowed from both conservatives and liberals, although it seems that both sides would see them as taking the worst parts of both and making it into their own thing.