Stress. Stress definitely weakens the immune system but it is considered a minor weakening, definitely not to the point of a true immune deficiency.
Impaired immunity. There is evidence of immunity impairment caused by all environmental stressors. Most studied is radiation. Uv light, extreme cold and hypoxia also show measurable decreases of immune responses. Usually they are mild, non-specific and related to time of exposure. Chronic stress, emotional or environmental, increases cortisol levels which reduces inflammatory responses.