Most US children (89.3% in 1993) go to public schools, which can range from excellent to horrible.

There are many alternate schools in the US. Most are sponsored by churches, but have differing levels of religious instruction. For example, the Jesuits run a Catholic high school in Dallas, Texas which is one of the better schools in the area, and a large number of their students are not Catholic.

Most states also allow home schooling. These results vary greatly with the capabilities of the parents.

There is a lot of media publicity over a very small minority of schools that teach religious dogma over science and math. Most of the publicity is political in nature, and is designed to extrapolate the policies of a few into one of our political parties.

I would be surprised if more than a few thousand children are involved (out of 300M Americans). I work with a lot of children from differing backgrounds, and I have personally never come across one of those cases.