That would imply that life in the US ~300 years ago, when pretty much everyone belonged to a church, was less dog-eat-dog.

If anything, I would say it was the opposite. People would often shoot someone—someone who is just as likely as themselves to be a "good Christian"—just for being an interloper on their farmland, i.e. for having the opportunity (whether they took it or not) to make off with some of their turnips.