Personal Life Dealbreakers for Academic Jobs
I am not a lawyer, so take this with a grain of salt.

In the US it is illegal to take information about a candidate's membership in a protected class as a basis for hiring or firing, except in circumstances where that information concerns what the law calls a "bonafide occupational qualification." 

The idea is that certain kinds of employers get to discriminate in ways that would otherwise be illegal because of their status as private entities dedicated to a particular mission. For instance, a Jewish synagogue can discriminate against non-Jewish applicants when it is hiring a rabbi. If the state prosecuted synagogues for religious discrimination because they only considered Jewish candidates, this would effectively be the state saying that Jewish Synagogues can't exist. 

So, in certain kinds of religiously affiliated schools, it is legal for the school to hire only members of a certain religion based on the same principle. But this only holds if membership in the religion is an explicit, advertised condition of the job, i.e. if the school is dedicated to being a school exclusively consisting of members of that particular religion. 

Most religious schools in the US are not actually like this--for instance there are dozens of catholic schools in the US which are open to students and faculty of any religious tradition, or no religion at all. Schools like that are not allowed to discriminate on the basis of religion, because clearly at such schools membership in the religion isn't a "bonafide occupational qualification".