First, "more angry" is acceptable, and referenced as such in the Merriam-Webster learners dictionary.
And there is a slight difference between "angrier" and "more angry", the former representing a strict comparison ("angrier than ..."), the second expressing an escalation in the degree of anger felt (compared with the same anger felt before).
It is that "escalation" which is easier to represent with the "more".
"When she heard the other story, she became angrier" (or "more angry") — in either case, I see "escalation".
Actually, I would find "angrier" more appropriate because of the comparison between the two stories (causing the anger to rise).
I would use "more angry" where there is no direct external comparison element (as in the OP's question: "They were more angry with Washington".
When you compare anger with anger, "more angry" makes sense to me.
If you compare anger caused by an external element with anger cause by another external element, "angrier" seems more adequate.
Or "Jack was angrier than Jill" / "Jack was more angry than Jill" — in either case I see comparison. So what's the difference?
Here, "more angry" could be used (if only "anger's people" is compared), except if your sentence go on with some explanation for said anger.
"Jack was angrier than Jill because of ..."
Keep in mind this is not an official rule, just my interpretation of how one could choose an expression over the other.
Both can certainly be used without real issue.
My point is just that:
- "more angry" is not "false"
- "more angry" could be seen as a "general way" to characterize a state of mind, whereas "angrier" would be a more specific way to compare the consequence of two external factors.
In that way, I don't think one is a "subset" of the other. They can be used to express two different situations.