There might not be a more unique, or controversial, human resources chief than Snap’s Jason Halbert, a decorated ex-military officer who served two tours in Afghanistan.

Mr. Halbert, who came to Snap with no experience in corporate human resources but is close to CEO Evan Spiegel, is infamous for regaling the staff with military stories that range from odd to inappropriate, according to interviews with nearly a dozen current and former Snap employees. To many, he reflects an increasingly combative and paranoid company culture that has driven away several experienced executives and drained morale.