Definition of "belief system"

I believe that a belief system is more subtle and less well-defined than you suggest. Judgements about right and wrong are not simple, and are not necessarily part of personal goals and objectives. To believe that it is wrong to covet another's spouse does not inhibit many people from their aim of enthusiastic adultery.

Nor is the distinction between true and false objective. There are still people who believe that the Earth is flat, despite all evidence to the contrary. There are those who believe that vaccination is part of a subjugating conspiracy, despite there being no evidence to support such an idea. There are people who believe capitalism is the best system, and others who condemn it. Brexit is pure genius; Brexit is stupid self-harm. And so on ...

A google search will easily reveal some of the complexities and varieties of "belief system". Essentially, it is a set of personal beliefs that condition how a person thinks, how they act, how they relate to others, what they think is morally good or bad, what mental model they have of the world. It may rest on sound principles and reflection on evidence or it may rest on prejudice and blind faith even in the face of good evidence to the contrary.

The second part, however, looks to be about objective reality,

I see this as an error: It is nothing to do with objective reality: it says "The belief system of a person [...] is the set of beliefs that they have" I may believe that black cats are unlucky; that there are gods, fairies and gnomes; I may believe that if I jump up and down three times, I will never have a cold.