I don't know understand why sympathetic stimulation constricts pulmonary vessels? I thought that the sympathetic nervous system activated the body for physical activity. Physical activity would need more oxygen supply. Doesn't constriction of pulmonary vessels reduce the gas exchange?
The sympathetic nervous system mediates the fight, flight and fright response. It constricts the arteries and arterioles to increase blood pressure, in turn pushing the blood to the muscles and other organs vital for physical activity.
The sympathetic nervous system functions triggers the fight, fright, flight (FFF) response (Fig. 1). It provides the body with a burst of energy so that it can respond to danger (source: Harvard Medical School).
The FFF response is initiated in the hypothalamus by activating the sympathetic nervous system through the adrenal glands. These glands release epinephrine (adrenaline) into the bloodstream. Epi increases heart rate and blood pressure to push blood to the muscles, heart, and other vital organs. The person also starts to breathe more rapidly and the small airways in the lungs open up. This way, the lungs can take in as much oxygen as possible with each breath. Extra oxygen is sent to the brain, increasing alertness (source: Harvard Medical School).
In blood vessels, as you say, sympathetic activation constricts arteries and arterioles (resistance vessels), which increases vascular resistance and decreases distal blood flow. When this occurs throughout the body, the increased vascular resistance causes arterial pressure to increase (Klabunde, 2012). This enhances the distribution of oxygen already present in the blood. I don't think the pulmonary circulation responds differently than that in the rest of the body. The stress response is meant to support the evasion of acute dangers. But indeed, chronic exposure to adrenaline may eventually lead to impaired oxygen exchange in the lungs (Krishnamoorthy et al., 2012).
Fig. 1. Fight, flight, fright response. source: Freelap USA