Now, YOU reaqd it...without a biased down-on-bible-thumpers view
I didn't see where pdr's interpretation had anything to do with being down on bible thumpers, nor that observation of the Sabbath was being portrayed as odd or droll.
To a religious person, limiting activities to what's proper is a way of raising one's children not only to be good in this life but to put them on a path toward eternal salvation. To a person with different views, the restrictions may seem arbitrary, pointless, rigid and cold-hearted, but that's a difference in viewpoint and not a difference in fact.
I posted the quotation from Lydia Child because her book was just behind me on the bookshelf, and I remembered she had a long passage on the subject which gave positive ideas for children to observe the Sabbath, and it was a close-to-period description that roughly coincided with Methodist views, though as I said, I didn't know if she was a Methodist herself. I'm writing about a couple of strict Methodist families myself in the 1850s U.S. right now, so am dealing with similar issues.
But before we rely on that quote too much, I looked up
the religion of Lydia Child just now and, as I suspected, she wasn't a Methodist herself. She was raised Calvinist and Congregationalist and was influenced in adulthood by Unitarians and Swedenborgians, though never seemed to have found a religion she could truly embrace.
So her quote can only be used as a general idea of typical observation of the Sabbath for children in the 19th century, but no more than that.
I'd guess the reason that a walk should be with parents or someone responsible is, that if a boy goes out alone, how can one be sure he's
not out bird-nesting or worse? Even if he's entirely trustworthy and the parents know it, why would he need to go alone, and wouldn't neighbors wonder what he's up to, seeing him wandering aimlessly about by himself? It would be like letting a boy and a girl go out alone--they may know they're doing nothing wrong, their parents may trust them, but why give the wrong appearance and why risk temptation?
A boy in such a family would know that, and so if he decided to go wandering out on his own, even if perfectly innocently, he'd realize he was being disobedient, and it would be for the willful disobedience that he'd be punished, not
just for the activity of taking a stroll.
I think the quote I posted about the Methodist preacher recalling his guilt for breaking the Sabbath is an example of the positive result of this kind of raising--at least "positive" from his viewpoint. His guilt was so great that he didn't need to be punished; he punished himself and resolved not to do it again, and stayed with his religion long enough to become a preacher himself.
It's certainly not what would be advised in a typical modern book on parenting, but it works within the context of the social situation and the period.