From a literal/historical perspective:
Due to the unexpected aspect of sniper fire, high lethality of aimed shots and frustration at the inability to locate and attack snipers, sniper tactics have a significant effect on morale. Extensive use of sniper tactics can be used as a psychological strategy in order to induce constant stress in opposing forces.
One may note that by many aspects (constant threat, high "per event" lethality, inability to strike back), the psychological impact imposed by snipers is quite similar to those of landmines, booby-traps, and IEDs.
Historically, captured snipers are often summarily executed. This happened during World War I and also during World War II. As a result, if a sniper is in imminent danger of capture, he may discard any items which might indicate his status as a sniper. The risk of captured snipers being summarily executed is explicitly referred to in Chapter 6 of US Army doctrine document FM 3-060.11 entitled 'SNIPER AND COUNTERSNIPER TACTICS, TECHNIQUES, AND PROCEDURES':
Historically, units that suffered heavy and continual casualties from urban sniper fire and were frustrated by their inability to strike back effectively often have become enraged. Such units may overreact and violate the laws of land warfare concerning the treatment of captured snipers. This tendency is magnified if the unit has been under the intense stress of urban combat for an extended time. It is vital that commanders and leaders at all levels understand the law of land warfare and also understand the psychological pressures of urban warfare. It requires strong leadership and great moral strength to prevent soldiers from releasing their anger and frustration on captured snipers or civilians suspected of sniping at them.
The negative reputation of snipers can be traced back to the American Revolution, when American "Marksmen" would intentionally target British officers, an act considered uncivilized by the British Army at the time (this reputation would be cemented during the Battle of Saratoga, when Benedict Arnold allegedly ordered his marksmen to target British General Simon Fraser, an act that would win the battle and French support).
Just sayin... snipers can rattle people.