In the context of religion, I prefer the word "faith".

Faith is a neccessary emotional defense, and it's necessary to learn anything as well. Not all topics are self-evident, after all, especially when trusting others about social norms growing up.

Though faith should NEVER be a method of reasoning, and that's exactly what organized religion teaches.

In college I was taught that a belief = a good reason:

Good as in the traditional Greek sense that the end is either the truth or the flourishing of people, including any instruments that serve as a means to those ends;

Reason as in a cause originating in the mind that influences action or behavior.

So if you had a belief of something, you had a good reason to do something. Believing is good reasoning.

Obviously, you can easily devolve into moral relativism here, so I think the Aristotelian school can ground us again, favoring perception, deduction, and induction to get at "objective" reality, like you say.

The issue is when pundits and rhetoricians hijack these projects by basing them on religion or political party, using language and pseudo-logic that can appear as trustworthy to those easily convinced.

I like your description of ideas though. This sort of concept has been jostling around in my head for a few months. Appreciate the illustration!

I'm not sure what your last sentence means. Belief as a bare concept isn't the problem. The problem is when people get together and start reinforcing beliefs that are based in nothing but "faith".

Religion is bad because it teaches that faith is equivalent to or superior to knowledge. Just by the very act of institutionalizing faith-based beliefs, let alone all of the religions that DIRECTLY say faith is superior.