For middle and high school, I went to a "
St. Grottlesex" school. The one I attended required everyone to attend chapel, and the only worship option was Episcopalian. These days, everyone is still required to participate in some sort worship services be they Episcopal, Jewish, Roman Catholic, Buddhist, Muslim, and several others.
Back in my day, attending chapel was mostly catechismal and dogmatic. These days, doing so is as much about theism as it is about reinforcing the school's human development and pedagogical approach and objectives. Spirituality of some sort is (1) deemed essential to one's development into a mature and stable adult, and (2) insofar as notions pertaining to theistic beliefs and belief systems make excellent foils for rigorous abstract thought, participating in worship services contributes to a student's intellectual development by providing them with foundational and contextual "ammunition" useful for considering myriad subjects they'll study and discuss -- ethics, history, politics, normative economics, biology, etc. -- in and out of class and well after they graduate.
In short, the school doesn't stipulate what one believes, or even that one believe; however, the school does mandate what one must do. What one must do is attend some sort of worship service. Whether s/he "buys into" what's said there is up to the student; the school doesn't care whether one is a true believer. The school is not about inculcation; it's about education, and spirituality and giving students a strong understanding of what that is and how it works is just another thing to teach and one must participate in it somehow to understand it.
Two of my sons were Episcopal enough (indifferent enough?) that attending Episcopal services didn't overtax their sensibilities, and from time to time, they'd attend a different belief system's services. My other son and daughter at an early age didn't "buy into" religion, so we sent them to non-denominational schools.
I suppose some parents may know their kids are atheist/agnostic and send them to "St Grottlesex." If they do, I don't know how those kids there these days handle the worship requirement. I presume they just pick a worship service and attend it because attending no service is, AFAIK, simply not an option. At least it wasn't when my sons were there.
Regardless of how agnostic/atheist kids reconcile the worship requirement, attending services surely does them good. How so? Well, as I said, the school is about educating kids. One aspect of that education is teaching them not how to rail against and fight "the system," "the game," but rather how to be excellent "players of the game," how to make the most of what "the system" offers. Being able to "relate to" and understand theists and how they implement their theism is part of that (It's not the "biggest" part, but it is part.), and learning those lessons firsthand, which frankly isn't a textbook or classroom learning thing, is, IMO and the school's, better commenced and mastered as a minor than is starting that process as an adult.
Does the "St. Grottlesex" approach constitute forcing religion on someone? Probably, though I think its a different modality of forcing it. Indeed, I'm not convinced one could call it forcing religion as much as it's forcing spirituality. All the same, no, I didn't force two of my kids to attend "St. Grottlesex." They were pretty clear about their religious views and I just thought there wasn't much point to pushing it on them. Though I agree with the pedagogical approach at "St. Grottlesex," I realize it's not at all the only one that produces very well developed and well prepared high school graduates.