I belong to a side which uses red make up, because that is what dancers in Leicestershire used (originally sheep raddle). Am I then to change this for fear of offending native Americans?

Don't be fatuous. There is neither accusation nor evidence that red-face disguise was taking the piss out of Native Americans, it is clearly a genuine medium for disguise and we all know it. There is however accusation and supporting evidence that black-face is/was associated with mocking black folk. Those concerned about blackface are advocating the use of other colours, like red, as equally/more authentic and entirely uncontroversial.

This is not the sixth form debating society, so don't start on the "what is black/red/yellow skin" nonsense. We are debating minstrelsy and related racist behaviours and we all know what we mean by "black" in that context.