Hospitals and Schools mostly owned either government or Religion Charities?

Most of the hospitals near me are owned by private health care companies.

Public schools exist to educate the population.
Private schools exist to make a profit, and in many cases, to indoctrinate children.
Hospitals make money for their owners.

Catholics ARE Christians.  Why do you need to separate them out?  One of the biggest hospitals in St. Louis is Jewish.  

Government encroachment.

Yes, but I suspect that it is not because of the reasons you are thinking of.