Why does stress impair judgment?

Actually, it depends. The yerkes-dodson curve (google it) says performance peaks with moderate stress — not too much or too little. But the best amount depends on the task. Judging simple, over-learned tasks can be done under relatively more stress; complex, novel tasks need much less. The "why" involves the effect of stress hormones & the sympathetic nervous system on cognition: emergencies call for fast action.
Brain function. There's an optimal range of "stress" that can keep you on your toes, but not overwhelm you. In this zone, you have the full function of your cerebral cortex, allowing innovative solutions to problems you face in everyday life. But when you're over-stressed, you go back to habitual patterns which may not be healthy. More automatic places in your brain can hijack your better judgment.