There's no such thing as being "officially recoginized" by the government as a religion. The old Soviet Union registered religions. We don't.
Receiving an IRS tax-exempt employer identification number is a completely separate issue and has nothing to do with government recognition of the validitity of a religious institution or belief. That is simply an administrative matter that has to do with 1) has someone applied for a tax-exempt employer ID and 2) do they administratively qualify under the law? The law grants such exexmptions to a number of different kinds of organizations, not just religious.
Free exercise rights under the 1st amendment belong to the individual, not to an organization. That is, the right belongs to the individual to believe/practice however they see fit. The government has no business saying, "You're a Catholic and good Catholics don't do x" or "You're a Baptist and good Baptists ought to believe y". The government is not in the church discipline business.
If you were to say "I'm a Wiccan and go to Mass on Sunday and I keep kosher and I observe Ramadan every year" so what? As an indivdual, I might think that's messed up, but I certainly don't want the government making decisions about what is good or bad theology.
The basic principle in this case is that parents - not the government - ought to say what religious instruction children receive.
A judge has no right to interfere with the religious..or non religious..upbringing of a child by their parents. If the private school wants to make criteria for admission, that is their business. to the judge on this: BUT OUT!
I don't want the State in my bedroom, my doctor's office or my kitchen, etc. If I commit a crime that hurts another, ok, step in. Otherwise leave us alone!