The term tar baby has gone off-limits. Old guys like me might still get away with using it, because we grew up in an era where the term had not the slightest racial connotation. Tar baby referred to the mute human mock-up made of tar in the Uncle Remus stories. Br'er Rabbit got angry at its insolence and hit it, getting stuck. The more he hit it, the more stuck he got. The point was that he had gotten himself into difficulty of his own accord, and was now in a problem he could not get rid of.
The irony, of course, is that Joel Chandler Harris likely reworked an image that he had learned from a black storyteller. The tar baby was black because it was an image of a human in an African-American context. In the same way that Crayola and Johnson & Johnson decided that "flesh tone" was a light tan years ago, neglecting to note that it was not the color of the flesh of a good many of their customers, a black storyteller, when describing a mock human, would of course make him black.
When I looked it up, I found isolated incidents that might have been racial slurs in the use of "tar baby" over the years, but it was a brand-new idea to me just a few years ago. Either someone used it racially to insult a black person, or some black person thought it was a racial slur, and the whole thing snowballed. The most likely explanation is that there were elements of all three - people known to be prejudiced used the term about individual black people with the primary intent of merely describing them as difficult; a hint of racism under it was not wholly imaginary.
It is no good saying that "tar baby" is not racist because it "really" means an inextricable problem in its historical context. Words change, and this is exactly how they change. Legitimately or not, the phrase has acquired a racist connotation. Individuals unaware of this might still use it in innocence for many years to come if they never run across any whisper that it has changed. Mitt Romney was called on the carpet about its use in 1999, I think ridiculously. The papers were full of people claiming that it was an obvious racial slur, as if this were something generally known. Rubbish. I am pretty alert to words and their connotations and I had never heard this before. He was using the term entirely in its older meaning, and some folks were just looking to be offended.
Once these things get started, however, they make themselves true. I would no longer use the term on the chance that someone would take it as racially charged. It's a pity, for we lose a vivid image in our common culture - one that African-Americans gave us, likely. But it now has that connotation, just as gay now means something other than happy, and atoms are known to be divisible, even though the word's origin means uncut or indivisible. It is no good saying that gay "really" means happy anymore than it would make sense to deny the existence of electrons because the word atom means indivisible.