One of the young men in my ward served a mission and graduated from West Point before going on to serve in military. I joined the church after I got married and had 3 sons. As a DoD contractor, I've delivered software to sites at SHAPE in Belgium, Ramstein in Germany, Naples in Italy and Izmir in Turkey. My next destination was Mod UK, but I had to defer so we had travel money to cover another employee for another site. Some other projects put my on aircraft that required survival training at PAX. Not a full time military career, but I did grow up in a Navy family where my dad was deployed half of my life.
My ward in Mira Mesa (San Diego) was full of Navy pilots from Miramar as well as some Navy doctors who were called to serve out of the country when things heated up for Desert Storm. There's plenty of LDS people serving in the military. They aren't dodging service to go on missions.