Except "system" really isn't that. It's a general purpose word for a collection of interconnected things. Everything from nervous system to solar system to operating system to, yes, even plural system.
Also there's a difference between "I talk to spirits in my head" and "I share my body and brain with several people" - the second is a plural system. And not all people with CDDs are systems, or plural.
Most of my headmates identify as being souls from another universe. Two identify as gods. I disagree but, that's what they see themselves as. If we just talked to each other, I wouldn't identify us as a system. It's the fact that we literally share a life that makes us a system. My headmates front for several hours a day without me being in front, and we share front for significant periods most days too. That's not a matter of religion, but of identity. Who "I" am, the person in charge of the body and brain, is not always the same actual person. And we're very different. Different genders, sexualities, personality traits, ways of thinking and behaving, and as already mentioned, beliefs.
It doesn't matter that I don't believe they're spirits from other worlds. It wouldn't even matter if I didn't believe I'm part of a plural system - I didn't see it that way for 25+ years.
Despite that, my experience is the same: that of being part of a collection of people in the same brain who work together.
It's definitely not the exact same as being a CDD system but that's the reason there's that initial qualifier. Just like how a solar system and an operating system aren't the exact same. A traumagenic CDD system and an endogenic plural system aren't exactly the same but they're still, like solar, nervous, operating, Internal Family systems etc, a group of interconnected things.
They're similar in other ways, too though, as both CDD and nonCDD plural systems are both collections of selves in one body and brain, and each self â whether person, part, entity, or alter â take recurring control of the body they share, with accompanying changes in personality, ways of thinking and behaving, and beliefs.
You don't have to believe the religion is true. But you must acknowledge that what CDD systems experience is in many ways similar to what nonCDD systems experience. True, not exactly the same, but again â that's why there's the qualifiers.