Schools have a responsibility to teach ALL students no matter their creed. However, I question why a student of a different faith would decide to join such a school.
Regardless, though, of the students' motivations, they have a right to get any sort of education they require/want as long as this education does not harm others.
I attended parochial school with kids who were Catholic & Protestant. Everybody was required to go to Mass, before class. But you were not required to join the Catholic church.
My own brood also attended private, Christian schools. One of the schools actually described itself as "non-denominational". During my son's elementary years, there was actually a Jewish child enrolled in the parochial school. Her parents, one Catholic & one Jewish, had chosen to expose her to both faiths simultaneously (and let her decide).
Christ, if you examine his actions & teachings, encouraged inclusion. Most Christian schools take this into consideration & attempt to follow the example. I'm not saying they all do so. However, from my experience, that's the norm.
While the separation of church and state exempts religious schools from government standards on the type of education or discrimination, there are exceptions.
For example, in many states the voucher system allows a student to take their state funding with them and choose a school. This means religious schools are getting taxpayer money through the back door without having to adhere to government standards. If a private school accepts taxpayer money, through grants or vouchers, they should have to adhere to government standards- including non-endorsement of religion and non-discrimination. Thus, a religious school shouldn't be taking students with vouchers in the first place because it is using taxpayer money to fund religious education.
A parochial/faith school should take in as many students as possible so they can have a chance convert them to their faith. You see when you control a child's education it becomes easier to get them to believe in any system you wish.
I went to a Christian school and they generally have one class on bible study and no one questions you on your beliefs they simply quiz you on the knowledge you learned from the bible in the class. I believe these schools would have no reason to turn down an atheist child and teach him/her the ways giving these children the option to choose for themselves.
The school I went to viewed the bible as a history book and not something to be worshiped or listen to as a form of command from god. My school even taught evolution is biology stating that days for God could easily be billions of years for man. That because old testaments was the eventual writing of word of mouth stories that translation could have been lost in many parts. The story of god creating light before the sun moon and stars could have suggested there was a flash of light before there were any stars in the sky. Than if you alter the order of a few verses which were told word of mouth so a lot could have got confused if you ever play telephone. Show the progression of evolution starting in the sea and working to the land animals.
Separation of Church and State isn't a One Way Road. The Church (religion) can't get involved in the State (government) and so the State can not get involved in the Church.
The State may not make laws regarding religion or religious institutions, regardless of how unfair it sounds. You can't kick the Church out, but let the State in...
People need to accept that a private entity, as a religious school is, should be able to act how it wants to. Should a school want to allow students of other religions to join, it should be allowed to as well. However, why would someone want to go to a school that will spread a religion that they do not agree with? Finally, they should not be able to deny a student on the basis of religious heritage, as many people deviate from their families' religious beliefs. Rather, it should be based on the individual person's religious beliefs.
Every child has a public school that will accept them. The idea of religious and private schools is that they have a specific type of education that they want to teach, and this may be for a specific type of community. They have every right to choose who they educate and who they don't. They are not depriving a child of their right to an education by not accepting them.