Sorry to bring up an old thread, but I had some thoughts that weren’t expressed above
Is atheism a belief system? No, it’s not!
Is theism a belief system? No, it’s not!
For something to be a system, it has to be coherent. Theism contains both belief in a single god and a belief in multiple gods. It can’t be a system.
Hinduism is a belief system because it has some level of consistency. Christianity is a belief system because it has some level of consistency. Buddhism is an atheistic belief system. Naturalism is an atheistic belief system.
But someone who believes in Naturalism can not be a Buddhist, so that makes atheism not a system.
And religions ARE belief systems. That means both atheism and theism aren’t religions, but each has religions as part of the category.