I have no objections to your term belief system.

Ultimately, however, I take the position that your distinction between religious, political, and philosophical, belief systems is arbitrary.

All of these belief systems are logical systems that can be traced back to at least one and sometimes multiple faith based axioms. The ardent Communist may hold of the Communist Manifesto and say true. The religious man may hold up his holy text and say true. The Nihilist Atheist may yell his belief that the universe is utterly random, he also holds onto his belief and say's true.

All humans follow faith based belief systems. Each individuals system is slightly different and they vary in their degrees of coherence.

Some faith based belief systems are more articulated then others with common principles that are written down and widely shared. Other individuals hold their core principles internally or follow them subconsciously. What is important is not whether the faith is written down that is just a reflection of how commonly shared the belief is. What is important is that individuals are aware of their faith and explore its logical consequences.

As far as I can tell our only real area of disagreement is whether individuals who follow a faith based belief system should be categorized as religious.

As the term religious is itself an arbitrary the various online dictionaries for example have 4-7 different definitions for this term. Exploring that dispute is not likely to be particularly productive.

You might find my recent post in the Health and Religion thread interesting. I was asked why I believed in God. This was my answer.

Why Do I Believe In God?.