How would you distinguish religious from non religious claims?

Personally, I think it makes the most sense to think of a person's religion as simply the sum of all their beliefs. In other words, everyone has a religion, and all beliefs are religious.

But if you are in charge of a content delivery system, you still need to find some criteria for determining which content people will find relevant. So the question is, what are the criteria that make a claim broadly relevant?

And I think a useful distinction to make here is that some claims are what I'll call "democratic", while other claims are less democratic.

Democratic claims are the type of claims that people can test for themselves or freely debate with other people without having to refer to a single authoritative source. Whereas less democratic claims are those that do not invite independent testing, or that only recognize a single source as authoritative. Democratic claims tend to be more broadly relevant, because people can test their validity and make sure they are useful and worth adopting to their worldview.

Science and engineering tend to make highly democratic claims, because they are readily testable. Whereas claims about current events and history are a little bit less democratic, but still fairly democratic as long as you have freedom of the press. While other claims, like those found in The Bible or the Quran, or the Book of Mormon, are less democratic, because they are not testable, and rely on a single, unquestionable, authoritative source.

The bottom line, I think, is that all claims are potentially religious claims, because they can be adopted into people's individual worldview. But some claims will be more relevant to more people. And the relevance of a claim largely comes down to whether it is freely testable and debatable.