Actually I think most charter schools are public schools - publicly-funded, not for profit, and free to attend, they just don't have to stick to as tight of a curriculum as the regular CRT LGBT communist grooming public schools do.
Charter schools and private & religious schools are separate things.
A comrade in my socialist org teaches at a charter high school and it sounds pretty cool compared to regular public school. One day each week, every teacher gets to teach their own (pre-approved) class with their own self-made curriculum -- so he's doing a course on the history of workers revolutions. Pretty cool stuff.