I would suggest that both Hilda Fish and Azizi are bright flames and very much on the side of the angels in this matter; Hilda recognizes with uncompromising keeness the use of some language to undermine or weaken classes and kinds of people by innuendo or tacit positioning.
However, there is (I think) a very clear and important difference in intent that must be taken into account. I have often sung "Pick a Bale of Cotton" with my wife and daughter on long road trips, in three part harmony, and I have often song "Wade in the Water" and "Keep Your Hand on the Plow" as well.
In every case I was singing to celebrate the song, and the music of it, and kick-ass spirit behind it. The idea that doing this is in some way a negative reflection or comment on African Americans, their grace, capability, or dignity, is laughable to me. It is possible that when you don't take intent into account carefully you end up holding onto hyper-sensitivities that are elective and arbitrary rather than being tokens of the context that actually deserves your wrath.
I cannot change the history of this country, but I could and did take action to change the state of civil rights in the 60's, and I have worked closely with people of every color under the sun from tar-black to red and yellow, and so far, after forty years of doing so, don't seem to have given any of them the impression I thought less of them, or was trying to pigeonhole them, because of their color.
The biggest thing any one person can do to counteract bigotry and prejudice and pigeonholing is to be alert to differences, and understand when things seem similar why they do, and seek to counteract the avid "associationism" of the unthinking side of our natures.
That would also include deciding to take offense at things and actions that are similar to, superficially, but in fact very different from instances of bigotry or racially-motivated condescension. Which might well include singing "Go Down Moses", "Jacob's Ladder", "All God's Children Got Shoes", or "Pick a Bale of Cotton", all of which I consider joyful musical treasures, not racial epithets.