In practice Faith based social services have existed for a long time--its called Voluntarism, people in their communities doing stuff with "public money", that isn't based on tax dollars, though . . . in some cities they are subsidized by tax dollars because its cheaper to fund somebody to do the work than get the governmental infrastructure involved. So tax dollars have been involved in what are referred to as "community services" for a long time.

As the Hebrew expression, translated into the English, the Faith card is the Same Lady with another Dress. I understand your reservations, just as I recall how Otto von Bismarck pressed for a Gesellschaft aka a State Bureaucratic system to cover Social Services because it standardized what was offered, providing statiility in the Reich. Gradually, the Gemeinde, the local community organizations were phased out to become what exists in most of Western Europe. The US is a little behind in that story, and I think as long as they are non-sectarian about their relgious attitudes we ought not have to worry.