Hi. I'm not from NJ, but there's a school called St. John Vianney near me, as well. I have to be honest, I've heard comments from people over the years about kids attending all different kinds of private and parochial schools, and how the kids at those schools are stuck up because their families "must have money to pay for tuition." My son attended a Catholic school because our local public one had a HUGE enrollment, and we wanted him to have smaller class sizes and some exposure to moral instruction as well solid academics. Were there some kids who seemed "elitist" and had a "better than anyone else" attitude? Yes. The thing is, the public school ALSO had cliques of kids who hung together based on their fancy brand-name clothes, etc. I think you'll find all kinds of kids at every kind of school.
My personal recommendation would be to have your kids do a "shadow day" visit where they "tag along" with a current student at the school you're considering, and see how they feel after experiencing it themselves.