I think this would have been a valid debate but on a more general tone.
If you take the bnp out of the equasion (and let's be honest most of us don't want to be associated with sympathizing with the bnp), there are lots of other organizations and religions etc which hold extreme views.
One of the 7/7 bombers was a teacher. He killed himself and many others in the name of Islam. Now while anyone with any inteligence knows that Islam is not all about extremist views, in reality, we don't know which muslims are extremists and which aren't, so would it not be safer to ban muslims from being teachers? Police officers? working in the public sector?
Many christian religions hold extreme views on issues such as cohabiting, homosexuality, some even believed that the disabled are so because of punishment for theirs or their ancestors' sins. So would it not be better to ban teachers/police officers etc from being christians?
The reality is that in all walks of life there are people with extreme views. And sometimes it's hard to identify who those people are, so we either have to ban all extreme views, and thus potentially freedom of speech, or we have to trust that most people working in the public sector, teachers, police officers, paramedics, doctors etc, are good people who either do not hold such extreme opinions, or who do not let their extreme views prejudice the way in which they do their job.