why would discriminating against poor whites be "purer" than discriminating against anyone else? Revealing use of language there.
Anyway, the short answer is that it's like winter fuel payments: lots of people don't need them but it would cost more time and effort to do means-testing than just to give them to everyone, using age as a criterion. Same here: rather than check everyone's bank statements, it's easier to assume that non-whites will be poorer than whites, as the statistics show, and use that as your basis, particularly if you've identified BAME people as the ones you need to attrract.
Cheap attendance at Labour party events isn't an inalienable human right.