Unfortunately most peoples ideologies are not expressed in the hiring process and few who interview that can figure this out conducting them. I suspect they’re trying to prevent further threats etc. so keeping her name out of the national news likely is wise.
I would think first off in the hiring process for teachers would be looking at their schooling which can many times give a view into their views on things. If they’ve ever been employed anywhere even as non teacher following up on references can add more insight.
The education process for teachers weeds out almost all who may have conservative points of view. This was of course one of the first targets of the Left.