Manipulating the law for Jesus.
You have to give the fundies some credit for their manipulative actions and the lengths of deceit they will go to in order to skirt the law.
Here is the problem. Government runs schools and it uses taxpayer funds to do so. That means all people, regardless of their religion or lack thereof pay for those schools. And since the rights of all people to respect their beliefs regarding religion must be honored then no specific religious belief can be promoted with those funds. What is done entirely in private is also of no concern to the state.
So for instance every mystic with his holy book, be it the Bible, the Qu'ran, the Book or Mormon, etc can pass out copies till the cows come home. Provided he does so on his time, with his own money, and on private property with the permission of the owner. And if he did this there would be no legal or constitutional issue as far as I'm concerned. And I doubt many others would find it problematic either.
I should note that while I'd respect the right of people to hand out any book they think is holy I doubt our fundamentalist friends would respect this right themselves. That is I suspect if someone was distributing the Qu'ran in some Christianist hell hole like Alabama they would be harassed by local Christianists resenting competition over the local yokels.
But in the civilized parts of America, outside the Bible belt, people would be left unmolested to pass out their god books. But the Christianists are a manipulative lot. They know that they have no right to use taxpayer funding for their message but try to find ways to bend the rules as much as possible. To me that is stealing. When they use taxpayer funds to spread their gospel they are stealing. They are using the funds of all Americans to finance their own message.
Now consider what happend in the Theocratic State of Arkansas, another Bible belt state with lots of ignorance, poverty and problems. In the backwater town of Mountain Home the Christianists used the school to distribute Bibles to students. It was done in a deceitful way which the Christians hoped wouldn't be notice. According to press accounts the school made an announcement to all students during their lunch, at the school, that Bibles were in a hall for free. The Christianists who arranged this said that because they didn't actually hand the Bible to the students it was then alright.
Now consider several facts. First, they still used state property to distribute the Bibles. School officials were paid to work for the school but used some of that time to arrange that the Bibles be brought onto campust, stacked in a hallway and then used more of that time to announce the free Bibles. So while their salary is tax paid their actions were for the promotion of one specific religion. In addition the students were a captive audience brought to this one place by state law.
The fundamentalist nutters know they have to grab kids young. Once the rational faculties are developed it is hard to find people willing to fall for insanity of fundamentalism. And schools are a prime target for these people who are constantly trying to recruit new members to their cults and sects.
Now if the Gideons or anyone else wanted to stand outside, off school property and give Bibles to students I wouldn't care. I'm sure some homes need extra fuel for the fireplace. I think they should be free to do that. But they are not free to use state property for ths purpose, not free to use state employees to announce it to a state mandated audience. So I think they violated separation of church and state on several levels. First, there must be no announcement in the school. Second, no distribution can take place on school property. But these recruiters are always looking for ways to force others to finance their missionary nonsense.