Difficult to believe in three main ways:
(1) By excluding a group from membership they are cutting off potential votes from part of the electorate. I would be unlikely to vote for a political party that would not have my friends or me as a member, even if I were sympathetic to its aims.
(2) By specifically excluding on the grounds of race the BNP makes it harder for itself to shed its racialist image.
(3) The unproven, sweeping generalities in the explanation given by the BNP make it difficult to take seriously.
However if the party strikes the right chord for you - and they would have you as a member - I can understand you voting for them.