I can speak to the Catholic school part of your question. My older son goes to a Catholic school in Berkeley. We are Catholic but we have a lot of non-Catholics there whom we are very inclusive of. The thing you need to keep in mind is that it is a Catholic school that is governed by the Dioscese so the curriculum & l a lot of activies are faith-based. The kids have religious studies a few times a week & once your child reaches second grade they prepare for Communion. Our non-Catholic kids participate in these studies but do not recieve their Communoin. The kids are encouraged & welcomed by our staff & Parish to line up w/the Communicants & get a blessing from the priests as well as participate it the celebration. We had a few kids not come to the Communion but come later for the luncheon. Our school is not all fire & brim stone so you'll have to seriously look at all of the schools you're interested in & ask how non-Catholics are treated & included as well as see their religious studies program. Our school does several commmunitry service project throughout the year: Food baskets for for the needy at Thanksgiving, books, clothing & school supply collections for Books for Barrios, Kids for Koins as well as a few others I can't think of now. But it's about giving back to the community & to those less fortunate than ourselves. My husband is not Catholic but is on board w/raising our boys as such & going to this school for the same reason as you...he wanted a school that talked not so much about God but more about being kind to others, etc & had a nice community. The school motto is 'Let's Be Go To One Another.' In the day & age of parents wanting a private school education, a lot of families are turning to Catholic schools cuz they are much more affordable than the 5 figure cost of most private schools. Keep looking at the schools you're intetrested in. Go on tours, ask questions. If you don't get in for K, you may get in for one fo the following years so make sure they know you're interested & keep applying. As you said, it's about the community & that's what my husband liked so much.
On the flip side, we sent our younger son to a Jewish Bridge K & I had to ask the same questions you have right now. He was warmly welcomed into their loving, caring community & happily took part in all of their religious celebrations. We personally liked that he was learning about another religion & their celebrations. Again, it was the caring, faith-based community that drew us in. Good luck!