This I think is teribly sectarian and mistaken approach to workers in trade unions and the Labour Party. I presume you were referring to trade unionists here "and the unionists for what it's worth" and not the loyalists in north of Ireland?
I agree that "independent working class political action" is absolutely necessary and fundamental to stopping the BNP- I presume you mean by this local campaigns, against e.g. cuts, against crime, againt poor housing. We should work on the estates etc and in the workplaces. However, there is nothing wrong with also approaching union activists- I'm not talking about the union tops but local activists and stewards. We do need an alternative and a break from the tory polices carried on by new labour.
However, it is also very important I think to have mass mobilisations against the BNP. Why? Becasue they are indeed as Attica's advertised call-out says murdering bastards and maximum organisation against them is necessary. Therefore the idea of chasing away people attending a UAF demo is laughable. One of the more militant antofascist demos I've been on in last 5 years was a UAF demo in Altrincham, Manchester and though the UAF leaders tried to prevent militant action most of the members of the demo took no notice.
http://news.independent.co.uk/uk/politics/article57648.ece
And the demos in Oldham in 2001 (pre UAF as it happens) whilst called by a local group included members of trade unions and members of the Labour party (including some of the Asian youth- well more the ones in their twenties) Should we chase them away? I'm all for political argument and it wasn't hard as many hated Labour for the war on Iraq, for poverty and all sorts of other things but to physoically divide the antifasvis movement would be a mistake- we should be for united action including as many workers as possible and political argument to form a new political alternative against the fascists and the capitalist politics that lead to them.