You know how 'blackface' - the practice of white singers and actors darkening their faces to act black - is now so taboo as to be a career-ending move? Well, there's a very good historical reason for that taboo: a genre of music called minstrelsy.
Put it this way: you know how the post-Reconstruction racial segregation laws are called 'Jim Crow'? That name comes from a 'minstrel' song called 'Jump Jim Crow'. This was written by Thomas Rice in 1828, in imitation of a song he heard from a black stable worker in Louisville, Kentucky. Rice would perform it in blackface, wearing burnt cork makeup. This song was so popular and widely imitated that 'Jim Crow' soon became a pejorative term for African-Americans. Thus the naming of those racial segregration laws.
In 1843, Dan Emmett and his Virginia Minstrels established the first full-length minstrel show in New York. Anyway, the Virginia Minstrels would wear blackface, and would send up African-Americans while playing music that was directly inspired by African-Americans. White minstrel performers would visit plantations and study their music - and would go on to make fun of that music on stage in ways that were obviously deeply, deeply racist.
In terms of what the black music heard by white people actually sounded like, the Ted Gioia history of the delta blues, titled Delta Blues, records one view on what African-American worksongs sounded like in the era of slavery, according to a British author/actress, Frances Kemble, who was staying at a Georgia plantation in 1839:
I have heard that many of the masters and overseers on these plantations prohibit melancholy tunes or words...and encourage nothing but cheerful music and senseless words, deprecating the effect of sadder strains upon the slaves, whose peculiar musical sensibility might be expected to make them especially excitable by any songs of a plaintive character, and having any reference to their particular hardships.
Elsewhere, Gioia explains that:
...above all, the various accounts that have survived from letters, journals, and publications convey the extraordinary richness and inventiveness of this music. When deprived of instruments, the plantation slaves would rely on their bodies for an endless range of musical effects: striking their thighs, clapping, patting their feet, whistling, vocalizing, and so forth. Happenstance objects would be transformed into musicmaking devices. William Cullen Bryant, in an account from 1843, describes a slave who made music for other black residents by whistling and beating two sticks on the ground. We hear also of musicians playing bones, or panpipes fashioned from reeds, or other instruments constructed from gourds, jugs, cans, pie tins, shingles, pieces of wood, whatever might be at hand. When they had access to formal instruments, the black underclass mastered these as well, and the literature provides accounts of slaves playing everything from the piano to the bagpipes. But (prefiguring the later preference of blues musicians) string instruments were the most popular and the easiest to obtain. In particular, the banjo and violin held pride of place at plantation entertainments.
Anyway, in terms of how this music was perceived by other whites, Dan Emmett's minstrel shows were enormously successful, spurring many imitators. This was a genre of music that would be very popular for close to a century (for example, Nick Tosches' book Where Dead Voices Gather profiles a blackface minstrel performer from the 1920s, Emmett Miller; you can hear a recording of Miller here). Gioia says that it was popular basically right up until the early talking movie The Jazz Singer featuring Al Jolson performing in blackface. Perhaps ironically, given that The Jazz Singer featured a performer in blackface, the movie essentially set in motion the decline of the traveling troupes in favour of Hollywood musical spectacle. The last documented performance by a minstrel group took place in Iowa in 1951.
But before The Jazz Singer, blackface performers doing minstrelsy would tour around rural America as part of medicine shows, or as minstrel shows of their own. These tours were enormously popular - often they were the only touring entertainment that would come to many rural areas. For much of rural white America, long after slavery, much of their perception of African-Americans came directly from these shows, according to Gioia:
For many Americans, especially those outside of the South, their attitudes toward the country’s growing slave population, their sense of African-American vernacular speech, music, and behavior, were shaped as much by these vulgar routines as by any firsthand encounters with black culture. And the medicine show, seen as appropriate family fare in most communities, brought these stereotypes to audiences that would never have attended a minstrel performance—indeed, even the pious “Quaker Healers” included blackface comedians in their shows, imparting an aura of religious respectability to the base proceedings on stage.
So yes, minstrelsy was black music adopted by white people in the antebellum era. It was enormously popular in rural areas in particular. And given the sheer extent of its reach and decades and decades of its popularity, it's very unsurprising that it was deeply influential on the rural white folk music that turned into country music - for example, one of Hank Williams's biggest hits was a cover of the Emmett Miller song I linked to above.