A person of specific faith, providing they are appropriately qualified, will always have an advantage over other candidates in an interview for that faith’s school. BUT…
That will certainly depend on the person being an appropriate appointment.
In other words, if that person is not a good teacher, then it is doubtful that the school will hire him/her over another candidate, even if the other candidate has no faith.
Being an atheist is NO OBSTACLE to being hired anywhere, as long as the person is positively disposed towards the ethos of the school.
I am directly aware of a Catholic institution employing more than one Muslim, as well as a good number of atheists, and others of different faith backgrounds, with no issues at all, other than the requirement that they be interested in good teaching and content.of course if one of them began to prosthelytise, that would be an issue.