For example: two are arguing and one makes a personal attack. They both become angry causing neither to speak reasonably.

Any word for this?

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EDIT: In my example, instead of 'angry', I should have used the word 'indignant'. I wasn't looking for extremes, like 'seeing red' or 'blinded by rage'. 

I also find 'enraged', 'infuriated', and 'apoplectic' not suitable. I'm looking for "a state of irrationality, caused by indignation."

From the responses so far, I think the best expression is "Their judgment became clouded by indignation."