Why are police officers banned?
They should be able to keep their political beliefs out of their policing duties, otherwise they are not suited to the job. Stopping them joining the BNP will not stop them holding racist views.
During the miners strike there was no call (by the mine owners) to stop police being members of the Labour party, nor were there calls (by the NUM) to prevent police membership of the Conservative party.

I see no problem with teachers being members of the BNP (or even the Labour party) as long as they leave their political beliefs at the school gates & do not try to indoctrinate our children.