Once more we have an argument for the state to fund private schools. This had a nice twist; the original prohibition had to do with a fear of a Catholic conspiracy. Whatever.
The simple fact is America has always believed in freedom of choice. That does not necessarily mean the funding should come from the public.
If you want to set up a private school because of your beliefs, in my opinion that is fine. Good for you! However, do not expect the citizens of the state should pay for it. Why should we? If your belief is shared by enough others, you will find the money to pay for it.