The singer at the underground party is based on Klaus Nomi, the German avant-garde singer known for his otherworldly stage persona, bizarre costumes, highly stylized hairdo that flaunted his strongly receding hairline, and wide vocal range. He often performed at the gay clubs and parties in East Village during the early 1980s before he passed away in 1983.
This episode particularly (and much AHS:NYC) mirrors much of the film Cruising. Cruising is about at NYC cop investigating a series of murders targeting Gay men.
The phrase "Thank you for your service" is usually given to Veteran Warfighters after being discharged from the military.