Depends on your definition of white :P I've got Irish and Italian blood in me. Historically, US immigration counted Italian immigrants as non-white, and Irish immigrants as "White, but we hate them too"

As for lack of culture/tradition, if I thought you were being serious, my response would be
vaffanculo and
p�g mo th�n
Or as an Australian, yes, jandals and BBQ do count as part of a culture. If you disagree, go to uni and ask a sociology or anthropology professor.
That does bring up a point though - the fact that white people often see themselves as "normal" and don't see their culture as being a culture itself often serves as a foundation to racism. It's easy to write others off as different when you don't see yourself as different. Totally mundane things that seem normal to you are often part of your culture that are alien to others. And just because NZ has a new culture that is heavily influence by other cultures doesn't mean it is any less of a culture.
As for "one of my own", I can understand groups feeling that way and have no problem with groups sharing in (and celebrating) that success. But frankly it shouldn't impact on team selection. A selector should pick the best team and a nation should support its best players.
SK, I get what you're saying by wanting sports to be more reflective of our national makeup. It's a nice thought, but IMHO it doesn't matter. All that matters to me is that if an individual wants to participate, they have the opportunity to do so, and that there are no barriers for them to succeed.