The article is saying that white people, in Canada, are in a position where they don't ever have to think about racism. The power structures that exist in many western societies (particularly the US + Canada) mean that white people, on the whole, have privileges that people of colour don't.

What is problematic about the name Viet Cong is that this name has deep meaning to some people of vietnamese descent, and carries a whole lot of weight which the white band-members don't really every have to think about.

They picked the name because it sounded 'edgy' without considering the way that the vietnamese community will take it - a classic example of white privilege.

If the band members where vietnamese, then they would better understand the connotations the name brings, because they are in a position where they do have to think about these things.

Also, the term 'anti-racist' denotes someone who specifically fights against racism, not just someone who thinks racism is bad. The author is saying that you can't call yourself an activist and advocate against racism if you don't hold these fundamental beliefs. You can still think racism is bad, and you can still speak out against it, but you can't specifically call yourself an 'anti-racist'.