There’s an interesting level here in that Jack tried to understand Christmas town. He could see the magic while he was there, and he did try to explain it that way to citizens of Halloween town. But they weren’t interested in the kind of life he was describing, so he started “rebranding” Christmas so that it was not like Christmas but was like Halloween. The people of Halloween town, never having actually encountered Christmas, have no way of knowing that what they’re being told about Christmas and “Sandy Claws” is inaccurate. Jack also tried to study Christmas and its culture, though he couldn’t quite get it; eventually, he literally decides to take it for himself, even as he knows it’s not really for him. He started out feeling sad the others in Halloween town didn’t ‘get it,’ but he then decided it’s not important to fully ‘get it’ but instead to have it.
So it’s not just accidentally removing things form their context; he has intentionally disregard the meaning of the rituals he purports to be recreating, making them more fun for the recreaters but not like what the rituals are supposed to be and without the related significance.