'they believe it isn't racist, [and]to concede the point would imply that it is.'
But supposing they are wrong in this belief?
You see in matters of promotion, you have to start with the perception of the 'market' and work backwards, to find the path down which you can send your message.
The 'marketplace' currently thinks blackface is racist.
It those sides had a budget to change that perception, they might do it - though it wouldn't be easy given the politics of some dancers and the historical facts.
But they don't have a budget. just a chance, not always taken, for some street crying. and those opportunities are reduced by, for example, schools not booking them because they present as intransegent.
The BNP does, however, have a budget, and is pushing at an open door.