If this were really about being 'woke', wouldn't it be a whole lot more obvious why the word 'black' in the song should be changed?
The reason that black sheep were less valuable than white ones is/was because black wool is more difficult to dye than white, so was harder to sell. I'm not sure that this links to the song in any way, which is about the wool tax of ages ago (#vague) when a third of the profit from a bag of wool went to the master (king) a third to the Church (dame) and the other third to the farmer (the little boy).
Neither the rhyme nor the idiom ever had anything to do with race, or even with the sheep - it was all about the wool, and the corrupt taxation in (I think) the middle ages.
Blackboards were changed to whiteboards not because of colour, but because of breathing issues for those who breathed in chalk dust all day. (Breathing in marker fumes may have had other effects, but perhaps they were more enjoyable ?).
Black binbags were and still are, just black. Because they are made out of black plastic. Which is black.
All of the above are very different from referring to someone as 'a Black', or worse, as 'a Black X'. Not the same thing at all, but it is in the interests of some to confuse the issue and make a mockery of anyone who wants to think about language and how it does affect people on the receiving end of thoughtless comments and outdated usages, such as obvious racial slurs, and words/phrases surrounding disability and sex (and/or gender).
If we are all tying ourselves in knots about sheep, or beanbags or coffee (for goodness' sake!) it distracts us all from the more important areas, and persuades us that we are being 'told' to do pointless things by 'experts' who are lacking in 'common sense'.