Black population in Western NC is small, so race wasn't very relevant to the election there either way. Being a Southerner and a Protestant helped LBJ along with his economic record and anti-poverty agenda.
This. It's worth noting that before blacks were truly fully enfranchised (i.e. 1968/1972 at the presidential level), areas with higher black populations would be the ones most strongly in support of segregationist candidates like Thurmond, Goldwater, Wallace, etc., because as you said, race was a much bigger issue and racism far more prevalent.
This can be best seen in Georgia, where the mountains of the North had virtually no blacks and were historically more Unionist. They had been traditionally very Republican to the point that not even FDR could sweep the region, yet in 1964 some of these counties swung insanely towards Johnson and supported him in landslides. Further south, in the more ancestrally "Dixie" part of the state, where the black population was greater and race a more salient issue than economics or foreign policy, it was literally the exact opposite and counties had, like, 100 point swings from Kennedy to Goldwater.
Appalachia has a whole had and continues to have a very low African-American population, which goes back to its roots as a region where slavery was far less common due to poor geography (which would also make these areas Unionist strongholds during the Civil War - for example, East Tennessee). So it makes sense that these areas supported Johnson strongly or, at the very least, did not swing nearly as hard toward Goldwater as the more traditionally southern, plantation-based-economy, areas of the Old Confederacy.