I don't know if they still offer this, but in New York State when I was a child, the public school children could come for religious instruction to the Catholic school down the street (where I was a student) once a month, before school was dismissed, and then return to the public school to catch their buses home. It was called "release time religious instruction" and was available to anyone who wanted to apply for it, not just Catholics. It required parental permission, in writing, and the students had to make up any work they missed. If the religious institution wasn't within walking distance, parents had to supply transportation.

It was an early dismissal day for those of us who attended the parochial school, and we dreaded it. Early dismissal was OK, but we all knew better than to leave belongings in our desks, or extra school supplies such as a large box of crayons, colored pencils of any description, or a nifty pencil sharpener, because those things would not be in the desks when we returned the next day. We all packed out the contents of our desks on those days.

About 10 years ago, here in PA, one of our elementary school principals attempted to start a similar thing for an evangelical group in the community, along with free transportation to and from, during school hours. I opposed it on the premise that, if it's to be release time instruction as I understand it, the school is not to promote or underwrite it in any way, including paid transportation. It eventually was dropped because of the acrimony the proposal generated. They may have had after-school instruction, but I couldn't say.

Parents are allowed to pull children out of class for all kinds of instructional purposes, so on its face this doesn't seem to me to be a Constitutional violation. If the school has set this up to be a "study hall" for the participating students, with no academic credit, it sounds like certain off-campus programs I've seen, in which the students may go places of their choice. If it's sponsored, paid for or allotted academic credit, I'd have second thoughts about its Constitutionality.