It appears that using black on the face is not, in itself, the problem. That link from Shrewsbury Festival says that it will not book sides using "full face black make up", but is happy with "other forms of colour and disguise"

So presumably the festival has no problem with sides that apply black to only some parts of the face (rather like military camouflage), nor with sides that use black and one or more other colours.

Both these alternatives preserve the element of blacking, while avoiding any implied racial mimicry, stereotyping or disrespect.