Therefore, assuming the first few statements, having an internally consistent belief system is desirable!
I think that's a straw man. Nobody denies that it's advantagous to have a consistent belief system. People rather argue that consistency isn't the only criteria on which to judge belief systems.
It pretty easy to make up a belief system that's internally consistient but that leads to predictions about reality that are wrong.
A good example would be the problem of hidden Markov models. There are different algorithms to generate a path. The Viterbi algorithm creates a path that internally consistent. The forward-backward algorithm creates a path that's not necessarily internally consistent but more robust against error. In my bioinformatics class we learned that for practical problems the forward-backward algorithm is often better than the Viterbi algorithm.
Fischer Black and Myron Scholes did work that gave financial traders an internally consistent way to measure risk. Nassim Taleb argues in his books that as a result the two reduced the resilience of financial models against errors and wrecked the financial system. To many people believed in the importance of consistency and as a result bad things happened.
If someone tells me there's global warming I'm much more interested in the question: "Is your model robust against error?" than the question "Is your model internally consistent?"
A lot of current social justice theory comes out of post-modernism which doesn't see being consistent as the prime value to which one should aspire. Political totalitarianism which presumes that the moral values of the population should be consistent got rejected. Multiculturalism assumes that it's good to have people with values that aren't consistent living together.
Making progress in accomplishing goals is a desirable thing. An inconsistent belief system will generate actions that are oriented towards non-constant goals, and interfere destructively with each other, and not make much progress. A consistent belief system will generate many actions oriented towards the same goal, and so will make much progress.
If you are wrong and focus on making progress as fast as possible, that's pretty dangerous. It's prudent to think a bit about minizing the damage that you cause when you are wrong.
If you are the social elite and are wrong, you do damage by forcing your values onto a minority that's right.
Often it's more important to focus on minizing the cost of being wrong than to focus on progressing as fast as possible towards some goal.
Usually, I don't get offended at things that people say to me, because I can see at what points in their argument we differ, and what sort of counterargument I could make to that. I can't get mad at people for having beliefs I think are wrong, since I myself regularly have beliefs that I later realize were wrong. I can't get mad at the idea, either, since either it's a thing that's right, or wrong, and if it's wrong, I have the power to say why. And if it turns out I'm wrong, so be it, I'll adopt new, right beliefs. And so I never got offended about anything.
Until one day.
One day, I encountered a belief that should have been easy to refute. Or, rather, easy to dissect, and see whether there was anything wrong with it, and if there was, formulate a counterargument. But for seemingly no reason at all, it frustrated me to great, great, lengths. My experience was as follows:
I was asking the opinion of a socially progressive friend on what they feel are the founding axioms of social justice, because I was having trouble thinking of them on my own. (They can be derived from any set of fundamental axioms that govern morality, but I wanted something that you could specifically use to describe who is being oppressed, and why.) They seemed to be having trouble understanding what I was saying, and it was hard to get an opinion out of them. They also got angry at me for dismissing Tumblr as a legitmate source of social justice. But eventually we got to the heart of the matter, and I discovered a basic disconnecf between us: they asked, "Wait, you're seriously applying a math thing to social justice?" And I pondered that for a moment and explained that it isn't restricted to math at all, and an axiom in this context can be any belief that you use to base your beliefs on. However, then the true problem came to light (after a comparison of me to misguided 18th-century philosophes): "Sorry if it offends you, I just don't think in general that you should apply this stuff to society. Like... no."
And that did it. For the rest of the day, I wreaked physical havoc, and emotionally alienated everyone I interacted with. I even seriously contemplated suicide. I wasn't angry at my friend in particular for having said that. For the first time, I was angry at an idea: that belief systems about certain things should not be internally consistent, should not follow logical rules. It was extremely difficult to construct an argument against, because all of my arguments had logically consistent bases, and were thus invalid in its face.
I'm glad that I encountered that belief, though, like all beliefs, since I was able to solve it in the end, and make peace with it. I came to the following conclusions: