I work for a school that does that not accept a dime of government money. We write, produce, and teach our own curriculum on the Classical model. We are accredited by three independent agencies. While recognized by the state as a school, we are not beholden to them in what, how, or who we teach. We obliged only to obey city fire, health, safety, and zoning laws, same as any business or public building.
There are many sacrifices. I will probably never retire. I'm poor as far as worldly standards. We don't have luxurious facilities. We aren't "up to date" with students using technology. (Students are not permitted to carry phones. They are turned off and kept in the office until dismissal time.)
We cover US grades K - 8. At present, all but grades 3 and 7 are full. There are two seats in grade 3, one in grade 7. The school opened in September of 1948 in response to concerned parents. We're proof it CAN be done.