I don't think you can have thought this through. The BNP have recruited a *tiny* number of Jewish people and publicly repudiated their traditional antisemitism, very obviously to reduce their menacing aura to respectable middle class voters, who are more likely to respond to an anti-mosque campaign than to an anti-synagogue one. They have as a party made no inroads in the Jewish vote at all. There is also the aspect of the global re-orientation of political forces taking place, in which the far right across Europe in particular is swinging behind Israel.
Incidentally, you saying they are "not really Nazis" is absolute uninformed nonsense. The BNP's origins lie in the fractious UK Nazi movement, from which their late leader John Tyndall emerged (the National Socialist Movement, the Greater Britain Movement, followed by Tyndall's briefly successful efforts to promote Nazi entryism into the NF which was then a 'traditional fascist' party, etc). It was founded as a quite explicit neo-Nazi party in 1982, bringing together two Nazi factions - the 'New National Front' and the British Movement. As such, the party always defended the Hitler regime which it hoped to reproduce. Tyndall himself declared that "Mein Kampf is my bible". The current media-friendly leader, Nick Griffin, is has been quite explicit in defending the Third Reich, protesting that it is unfairly maligned by an "evil hoax" (the Shoah) and suggesting that poor Adolf has not received his due credit. His cadre, the core of the leadership, have been caught on tape admiring the Nazis, executing Hitler salutes, celebrating his birthday, etc. Mark Collett, Griffin's number 2, has explicitly praised the Third Reich more than once. Many of the leading figures in the BNP have direct connections to Nazi paramilitary organisations, and Griffin himself has a history in this milieu. The violent Nazi group Combat 18 ('18' because the numbers one and eight are analogues for 'A' and 'H' in the alphabet) was founded explicitly to act as guards for the BNP leadership in public appearances, and they still perform this function today despite having diversified into terrorist campaigns. The public pretence of distancing themselves from Nazism and antisemitism is just that: a calculated imposture.