The difference between the organisations the BNP has listed in the link you've put up, Hamm, is that these are not political parties. You can't vote any of them in to govern the country. One treads a fine line between 'race' and 'culture' - I may well, for example, have been born in Africa (I wasn't, but many friends and relatives were), but white 'Africans' don't share the same culture as indigenous black Africans. Most white Africans are Christian, not animist, they won't share the same geographical and demographical heritage, and they don't share a historical belief in the myths and legends of African folklore. Therefore, if one is going to enjoy the clubbiness of a shared culture, one forms organisations which reflect mutual understanding - the Freemasons didn't exclude black Africans in Africa, but most black Africans had no interest in the Freemasons, because, culturally speaking, there was no shared historical heritage. However, white and black Africans do share business, professional, and sporting organisation memberships, because of a shared knowledge and interest.
Yes, you could say that any organisation which refers to itself by a racial denominator is 'racist', but do these organisations actually exclude membership to any other colour? I doubt that, by law, they can. Their aim is the promotion of support for the racial group mentioned, but I'm sure that if a white man wanted to be a member of the Asian Boys Society, he could join. He may well wish to do so if he were married to an Asian woman, for example, or vice versa, and wanted to absorb a better understanding of Asian life.
We still have women's only and men's only organisations which aren't illegal, yet they obviously exclude one gender from their membership - usually basing its attendance at any functions on 'guest' status.
As for the (inevitably) noted Jewish organisations - they're merely religious, like organisations for Quakers, Seventh Day Adventists, Mormons, Roman Catholics, Hindus, Buddhists, Muslims, or even Wiccans. There's nothing racist about calling an organisation Jewish, since it pertains to the belief of its members, not their ethnicity. There are Arab Jews, African Jews, American and European Jews - what unites them is being Jewish, as against being Baptist or Buddhist. Religious organisations would tend to be more exclusive, since by their nature, believers from other faiths are unlikely to join, any more than would atheists.
I say it's inevitable that the BNP would include Jewishness in its agenda, because there's no doubt that, in tune with most fascist and certainly extreme fascist, organisations, the Jew is still seen as a global evil - preferably one to be eradicated. Muslims will, equally inevitably, all be tarred with the 'terrorist' brush, and no doubt the BNP would like them to suffer the same fate as the Jews. They could have put up the logo for any Roman Catholic society, but no doubt know it suits their ends not to - however else might they appeal to the Catholic, so-called working-class conurbations of places like Liverpool, for example? As usual - seek out the beloved targets of all right-wingers: those damned Jews and blacks.