My daughter just started in a Catholic school. We aren't Catholic... but it's 2 blocks away and the public schools in my area are the pits.
They still have to adhere to certain standards in order to be accredited. I am not clear on what those standards are... I know they can and will teach some spiritual teachings.. but that test does cross the line.
I attended a non-denominational school in my high school years. That was 1976-80 .. and there was never anything approaching the test in question. It was the same material as regular high schools, more or less, with some scripture thrown in along with praying and wearing a uniform.