I suppose we can quibble over terms "mainly" and "neutral," but for the most part, the U.S. was largely concerned with only its own region and with its own interests. This also included freedom of the seas, which is how we ended up in such far-flung places as the shores of Tripoli. Note that this doesn't make the U.S. any better or any kind of paragon of virtue, as it also included numerous other wars and atrocities against indigenous cultures. But that, in and of itself, did not compromise our neutrality when it came to European conflicts.
For example, we stayed out of the Napoleonic Wars and other European wars throughout the 19th century. Our forays into the Pacific were slow and sporadic at first, as we got off to a bit of a late start compared to the major powers of Europe. There were numerous wars in Europe, Asia, Africa, and Latin America which we did not intervene or take any sides all throughout the 19th century.
I would say "mainly neutral" is accurate enough, given the US position relative to the rest of the world and the other events which were taking place on a global scale.
The main reason the Monroe Doctrine worked out was because Britain supported it and benefited by it. But overall, the overriding policy in America was to refrain from foreign entanglements and permanent alliances, playing no favorites of one foreign nation over another. "Manifest Destiny," in my opinion, was more of a propagandistic justification after the fact. Obviously, we didn't annex Canada (our one attempt to do so failed miserably). We ultimately reached a point where we could have a reasonably cooperative relationship which worked out for our mutual interests, as well as the interests of Britain.
Of course, as you correctly point out, by 1900, the landscape was rapidly changing, as the U.S. took on Spain in 1898 to get the last remnants of the Spanish Empire in America (Cuba and Puerto Rico). Taking the Philippines was a mistake. That's where we went beyond our reach. That's when we started to get more involved, particularly when we were part of a coalition of several nations involved in China, but even then, as you noted, we were just a bit player back then, punching above our weight. We were "mainly neutral" out of practical necessity as much as anything else.
Keep in mind that this is in context of an earlier point which used the term "isolationist." In describing earlier forms of US foreign policy, I would say "neutral" is a more accurate description than "isolationist." Based on the historical examples you've provided, "isolationist" would most definitely be incorrect. "Neutral" doesn't necessarily imply peaceful or unaggressive. It just means that whatever they do, they do for themselves, not in coordination with or for the benefit of other nations. "Non-aligned" is another term that might be used in more recent times.