Libertarianism can actually mean a lot of things, actually, but for the sake of this post, let's imagine that the American government as it originally existed remained in that form, that is, a small federal government with low taxes (including no income taxes), a mostly laissez-faire attitude toward business, and a non-interventionist attitude toward foreign powers, but otherwise as much as possible like America as we know it. If a science fiction story took place in a setting where America had followed that path (either through some kind of time travel intervention or quantum alternate universe), what would that look like--how would American Libertarianism have influenced world history?
First off, America's largest war, the internal conflict between the Confederate States of America and the United States Federal forces, would almost certainly have kicked off anyway. Some Libertarian types might argue that Federal overreach caused the war, because otherwise the North would have let the South leave the Union, thus no conflict. But the actual fundamental point of friction of the war was whether or not it's legitimate to consider another human being private property. To this, a commitment to follow Libertarian principles offers no unequivocal solution--thus I believe the war still would have happened...(please note that I am not a Libertarian, but do not consider myself inherently hostile to Libertarianism)
But without the expansion of federal power (under the Lincoln administration) that included the creation of income taxes to fund Union Armies, it's unlikely the North would have won. The history of an America split into two immediately becomes very difficult to predict. Certain Southerners always advocated expansion of the South into Latin America in order to counter-balance the power of the industrial North. If the CSA had won the war, it's hard to even guess what would have happened next--would the slaves have been freed eventually anyway, but live in virtual serfdom? Or eventually be equal citizens? Would the South expand into Latin America? If so, how much? Would Southern expansion cause another war between the USA and the CSA--or perhaps even a whole series of wars? Would an expansionist South eventually conquer a United States committed to limited government (and hence, a small military)?
To be able to continue with this thought experiment requires keeping America as much as possible like it is today, so let's assume that somehow the North won the Civil War anyway, perhaps through a temporary expansion of federal power that it eternally regretted afterward, going back to the small government the United States started with and never straying away from it again. So, America would exist as a nation from sea-to-shining sea, but with no later foreign intervention in the Spanish American War, thus no expansion into Latin America or the Philippines (and other locations in the Far East), so there would probably be no statehood for Hawaii or Alaska, and no Panama Canal.
A strictly neutral, non-interventionist, small government, 48-state America would not have built the large navy required to support the limited overseas empire our America had at the turn of the twentieth century. When World War I kicked off, not only would a non-interventionist America be unlikely to join Britain and France in a war against Germany, it would not have been able to fight even if it had wanted to, since it would not be able to defend its own troop transports against U-Boat attack (if it somehow it decided to violate Libertarian principles and enter the war). Without American intervention, it is virtually certain that Germany would have won WWI, which was a rather close thing as it was.
And what then? Germany winning WWI would not have destroyed Western liberty. German imperial ambition was to become a first-rate colonial power like the United Kingdom and France, to have the right to build its navy and expand it's commercial interests. It's unlikely they would have demanded permanent possession of the piece of northern France they occupied during the war--though they probably would have forbidden permanent armaments in regions bordering Germany and would have perhaps limited the British navy or something similar. That means the German Empire would have remained in Africa and probably would have expanded, possibly taking over French African colonies as recompense for returning occupied northern France to French control. A weak Spain, still corruptly in control of Puerto Rico, Cuba, and the Philippines (due to US non-intervention), likely would have lost these territories after WWI to an expansionistic Germany--though Imperial Japan probably would have taken the Philippines, as without America intervening, only Britain would have a major interest in curtailing Japanese power--but after a losing war with Germany, they would only have limited means to do so.
I believe World War II would have still happened, but not the way we know it. Consider that the conditions that allowed the rise of the Nazi Party were as much a product of the Great Depression and the post-war cultural malaise of Germany as of Germany's defeat. In other words, I think there still would have been Nazis or similar Rightist parties that would have challenged the authority of the then-legitimate German government. In my opinion, the Kaiser would do a better job controlling the expansion of Nazi power than the Weimar Republic managed, but I believe he would have done so by co-opting their nationalist positions and harnessing their energy, rather than by destroying them. After all, Communism swept through Western nations in the wake of its victory over Czarist Russia (in part because of clandestine support from the Soviet Union), and the Kaiser would want the help of Rightist militants to fight insurgent Communists and Anarchists in his empire. Keep in mind that Fascism took over Italy, which was on the side of the victorious allies in WWI, and did so without supplanting the monarchy, while vigorously fighting Leftist parties. On the other hand, it's possible that France or Britain could even have become officially communist states after a WWI defeat, but I doubt either of these nations would have ever become Communist in the Soviet sense or would have stayed in that camp for long.
So, a post-Great Depression Germany, influenced but not controlled by Nazis, surely would have declared war on the Soviet Union, the Rightists echoing Hitler's cry for "Lebensraum" in the East. The nations of Eastern Europe would face the hard choice of allying themselves to German power or being destroyed. After a loss to Germany the first time, it's possible France and Britain would never have dared to intervene. If they did intervene, a non-interventionist America would have guaranteed their defeat.
I think this would lead to the Soviet Union ceasing to exist, with a German-installed puppet government in Moscow, and probably the entire Baltic region dominated by Germany--and perhaps the Black Sea as well. Japan very likely would have taken this opportunity to continue to expand its empire in the Pacific region by conquering all of Russia that borders the Pacific Ocean. In fact, it's very easy to imagine the entire world-wide British Empire (and other European empires) eventually falling mostly to Germany but also to Japan.
In fact, I believe a historically non-interventionist America would have realistically led to a world divided into two spheres of influence. Japan would control the Pacific rim, probably including Alaska and Hawaii and likely Australia and New Zealand (and Southeast Asia). Germany would be the dominant power in most of Europe and Africa, have tremendous influence in South America, control part of the Caribbean, and would take the role in the Middle East that in our history had belonged to Britain and the United States. India might have a precarious independence between the two powers (or be German-controlled), but with China almost wholly subject to Japan.
Hypothetical science fiction story settings like this allow an author to comment on real world conditions. I think any realistic examination of the results of American interventions in our world show themselves starkly in contrast with a story world like this, showing easily that if America has always stayed non-interventionist, the world as whole would be much worse off. Much--most of the world would easily suffer under totalitarian control, ethic minorities would be brutally oppressed, and forget about any establishment of a modern-day Israel.
But the same story would show in fairness how many things in a Libertarian America would be better. Taxes would be very low, simultaneous with no budget deficit to speak of. Government social services would be non-existent, but church and charitable organizations would do a remarkable job of picking up the slack. American business would prosper--playing economic middleman between competing Japanese and German interests. And there would be no Defense Authorization Act, no government spying, no department of Homeland Security, and no intrusive checks at airports. Islamic terrorism would largely be a German problem and to a lesser extent, a Japanese problem (assuming they controlled the Islamic nations that in our world include countries called "Indonesia" and "Malaysia"). The throes of insurgencies fighting against occupying powers would be entirely their problem, not ours.
Since America would have a well-armed citizenry and a tiny but highly professional military, neither Germany nor Japan would want to invade us, because doing so would give the other world power an automatic ally, an economically powerful one. So they would leave us alone as they competed with one another to gobble up the rest of the globe. Unless, one of the two should somehow manage to conquer the other...then nothing would keep the militarily dominant (and overwhelmingly powerful) victor from adding the United States to its empire (perhaps in the story linked to Canada), fulfilling the strange ancient human greed to rule the entire world.
A story could be set on the cusp of a war that Americans in the tale believe will destroy the status quo and give, say, the Germans, supreme world dominance. The American characters in the story could struggle among (and perhaps within) themselves over whether or not the time had finally come for the USA to intervene on behalf of the weaker power, even though there has been no direct attack on US soil, coming to Japan's rescue before the balance of power has been irrevocably destroyed, before it's too late for America to be able to defend itself...