"Rio Grande," in my mind, occupies a sort of "neutral" space. This is subjective, I admit. Yet what I mean is that it doesn't suggest (again, to me) any particular national or ethnic connections beyond just being a common song of the varied lot of sailors. Maybe it's because it doesn't seem to have any land connections at all; it is a chanty, exclusively. The early chanties, in my experience, have a strong feeling of being connected to an African-American tradition or repertoire. And a lot of the late period chanties are borrowed land-songs, bringing with them the cultural associations of the land from which they came. That this has neither puts it in a period when chanties had become—or at least some had certainly become—"released" from the early associations (again, that I allege). They had become the shared genre. They were "generally" American, perhaps, as some 19th century writers did associate "Rio Grande" with American-ness:
If most of the forecastle melodies still current at sea be not the composition of Yankees, the words, at all events, are sufficiently tinctured by American sentiment to render my conjecture plausible. The titles of many of these working songs have a strong flavour of Boston and New York about them. 'Across the Western Ocean'; 'The Plains of Mexico'; 'Run, let the Bulljine, run !' 'Bound to the Rio Grande '; these and many more which I cannot immediately recollect betray to my mind a transatlantic inspiration.
[From Russell, W. Clark. “The Old Naval Song.” Longman's Magazine Vol 12 (June 1888): 180-191.]
Russell, quoted here, was English. Perhaps it is my American position that is preventing me from seeing anything particularly "American," as this is sort of my "default." In any case, if it were a halyard chanty I am quite sure it would strike me as a Black style of song, and if it had, say, Irish earmarks it might stand out for me. But it really does just appear as a "plain old, right in the center of the definition" capstan chanty...the Dunhill Standard Mixture! (Incidentally, "Rio Grande" also seems to be one of the most stable or consistent chanties with respect to its tune.) Funny. So whereas chanties like the recently discussed "Stormalong" and "Santiana" seem to reek of an earlier period (1840s)...and the sweat of Black labor in the Southern U.S...."Rio Grande" evokes the White American common sailor of the 1860s, by which time chanties had become a ubiquitous shipboard "tool" and originals were being created aboard ship. Or at least in my opinion.