I have two sons (the younger will start college in a few weeks). They both attended "activity" camps (daytime only, no sleep-overs) -- neither "religious" nor "anti-religious", simply "learning" -- nature, art, sports. I think they enjoyed these things, and that's what mattered (along with getting them safely out of the house during the summer).
I never attended any sort of camp as a child, except for one occasion, accompanying a few dozen Boy Scouts in southern California on a 2 or 3 day camping trip (getting far enough into a "wilderness" area, having tents, camp fires, hikes, etc). On one evening of that event, there was a "snipe hunt", for which the premise was that a creature was out there in the surrounding area that would be attracted by loud noise, and if we split up into groups of two or three, dispersed into the darkness, settled into positions far enough apart, and made as much noise as possible, someone might be able to catch a "snipe". Enough of us were gullible at that age, and the rest of us were content to play along. When we were called back in, the counselors let us in on the joke.
The point was simply that it was a joke, primarily for the enjoyment of the counselors: there can be general fun and enjoyment from playing innocuous jokes on gullible people, given that you let them in on it afterwards and keep it friendly. Lesson learned, no harm done.
For any "camp" experience to be based on (or directed by) a philosophical or doctrinal position is to do violence to the core value of a camp, which is that the attendees are being provided with a range of diversions. They should enjoy it, not be harmed or devalued by it, and develop friendships. If they happen to learn things, that's a nice bonus, but what gets learned is entirely up to each kid, not the planners.
Regarding the camp program cited in the OP, or any of the Judeo/Christian camps it is meant to contrast with, what would happen to a child who expresses a belief in reincarnation? If this poses a conflict with the goals of the camp (and has a negative impact on the child's experience), there is a basic flaw in the design of the camp.
autotelic adj. (of an entity or event) having within itself the purpose of its existence or happening.
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