We're thinking about this the wrong way. Aren't most of these racial and religious terrorists?
Australia's worst terrorist killed people in a place of worship. The Charleston Church massacre happened in a place of worship. Both shooters were also white supremacists (or white nationalists, which is a term that makes white supremacists feel better about themselves). In interviews and a written manifesto they repeated extreme beliefs shared by Murdoch-owned media and right wing politicians, sure, but the core of the issue is this toxic mix of racial and religious hatred.
On the other side, Islamic terrorist attacks aren't left wing. They want to impose religious rule, not communism or socialism. As do the extreme Christians that infiltrated the major parties in Australia. Scott Morrison's Religious Discrimination Bill 2019, for example, is a first step in imposing taxpayer funded religious rule.
