Hold on now - I said that Moore's action wasn't unconstitutional both because there was no legislative act, and because he was not administering a law. A public school principal has a legal mandate to provide a particular service, therefore he is administering a law insofar as he's providing that service. Note that he's not only prohibited from discriminating on the basis of religious views, but on the basis of any kind of views, so there's no need to fret over some imaginary secular/religious divide, as is being done now.
If the state spends money to hand out the Koran at school, that is not unconstitutional unless there is legislation authorizing the decision.
Absolutely no more unconstitutional than handing out The Communist Manifesto or The Origin of Species.
If the a sheriff arrests me for "disturbing the peace" because I am praying on the sidewalk, that is not unconstitutional unless there is a law against praying on the sidewalk.
A sheriff has no authority to arrest you for something that doesn't violate some law.
As for your definition of "religion," you sound like Judge Moore.
I wasn't trying to define "religion"; I was simply quoting back to you the terms you quoted to me: sect, society, denomination, mode of worship. They all have pretty self-evident definitions.
No authority doesn't mean it doesn't happen.