A Catholic educational system does not have to be neutral because it is a private as well as religious institution. It is therefore supposed to teach Catholic dogma, doctrine, discipline, practices, and customs. Hopefully, the instructors themselves are well-versed in Catholic beliefs and practice what they preach (teach).
However, the problem with teaching about G-d in a public-school setting is that each religion has a somewhat different understanding of the nature of G-d (or gods), apart from the different beliefs and practices within the religion itself. I would not want my children to be taught by public-school teachers who might favor a Catholic or otherwise Christian, Muslim, Hindu, Buddhist, or Baha’i understanding of G-d. Rather, I would want my children to learn about the Jewish understanding of G-d and the Jewish religion, and the best place to learn such would be in Hebrew school, taught by a knowledgeable rabbi, not by a possibly biased or ill-informed public-school teacher. I suspect you feel the same way about your children, as do Muslim, Hindu, Buddhist, and Baha’i parents.
The above problem was one of the dilemmas for Catholic children and their parents earlier in U.S. history, in that these children were forced to learn about G-d and religion in public schools from a purely Protestant perspective. As you’re probably aware, there was much animosity toward Catholicism altogether. Thus, Catholic schools were formed to teach Catholic children about their own religion, not someone else’s. Nonetheless, Protestant teaching about G-d remained in the public-school system for some time to come.
