Agreed, but I think just being a bit extra forceful or clear about the ethnic component when they share affiliation with a typically non white group like being Muslim or Chaldean Catholic.

Example:

"I'm a Muslim"

"Interesting, how did you come to those views?"

"yadayada"

"gotcha, well I just wanna remind you again that this group has a focus on members being of the European racial stock. Is there any conflict between your religious views and that idea?"

By doing that you aren't saying "bro are you sure you're white" but instead just sort of bringing it up yet again to make them worry in the case that they are non white.

I have zero experience as an interviewer, so ultimately my advice is with a grain of salt. I'm confident you and the interviewing staff will make the necessary adjustments if they are needed.