I know non-Catholics who have taught at Catholic Schools, and non-Jewish persons who worked for the JCC here, so it does happen. But a lot of jobs like church secretary, janitor, maintenance and the like tend to be held for people who belong to the parish (or congragation, or temple et. all.) who need the work.
But, first of all, churches and such organizations (like the Boy Scouts/Girl Scouts) have special exemptions written into the law which specifically allows them to discriminate on such a basis.
Second, the small business deal (under 50 employees) provides great latitude in such areas also, so its very hard to sue them. Larger companies would not care, or have other ways to get at that info without asking such a question.
Third, yeesh, I'd hardly be happy working for someone like that in the first place, so for me it would be 'good to know, I'm outta here!"