By Christian Muslims, I sincerely hope that they mean the the parents were a Christian and a Muslim, and not actually referring to Muslims as a ethnic group.
Part of her confusion might be explained by her constant references to the "Muslim race" and the idea that Muslims wiped out the Islams. She started out as an anti-Asian campaigner. Australia being "Swamped By Asians" was her warning (never happened BTW).
To her, Muslims are a race because she comes from a backwards rural white ghetto. She's from Queensland, which is Australia's version of being from Alabama. It's also the state that had the most Japanese investment 20 years ago, so there was a backlash up there against Asians.
But that was on the coastal city areas, and she's from the rural part of the state which didn't get the Asian investment (nor the Asian immigration, so you have to wonder why she cared). Her profession was running a "Fish and Chip Shop" before entering politics, and all the locals knew and voted for her. It's that type of backwards, up North.