There were and are still many times that Deaf people were not allowed to be in the military around the world, despite their desire to serve their countries, just because they are deaf. Time has changed some in some regions.
An early record of the American Deaf soldier is a famous American deaf hero Erastus Smith (1787-1837) commonly known as "Deaf Smith" for his significant role as a scout and soldier in the Texas Revolution. Captain Erastus fought for Texas' independence. In the civil war, "Deaf smith" was a influential soldier and helped Texas gain its independence.
Watch the narrative of Deaf Smith and his history.
In addition to Captain Erastus or Deaf Smith, there was a number of other Deaf soldiers during the past civil war such as Major-General John Barnard (Mexican-American War), Private William Berkeley (Civil War), John Blount (Civil War), William Chamberlain, Henry English, Private James George, James Jennings, James M'Farland (Dispatch Carrier), Benedict Oppenheimer (Field Artillery), and more.
Keith Nolan at TEDxlslay talks about his cadet experience.
In the U.S. and many other countries, Deaf people are not allowed to serve in the military. On the other hand, Keith Nolan explains that Deaf Israeli soldiers are allowed to serve in the military (The Israeli Defense Force) in Israel. E.g. 2nd Lt. Shira Kochavi is a female, deaf Israeli military officer in combat intelligence.
Nolan points out that American had Navajo Code talkers during the World War II. There must be something that Deaf people have their natural skills, such as enhanced visual-spatial processing abilities.
"The Department of Defense has been employing deaf Americans due to their natural strength to analyze intelligence photos and video." -- "Let Us Work: Deaf in Military" at 4:34 (https://www.youtube.com/watch?v=eXglHthScy0)
There appears to be a military's inclusive policies in Kenya that allows Deaf Kenyans to participate in its country's military services.
"Erastus "Deaf" Smith." http://www.sonofthesouth.net/texas/erastus-deaf-smith.htm