Yes, military service is compulsory in Israel so using "ex-IDF soldier" in this context does stick out because it isn't actually adding any new details. It gives the impression that the reason that language was chosen was that it implies something more nefarious than "Israeli" without the requirement of actually detailing what makes it nefarious.
When I discovered that Dr. Ruth Westheimer had been a particularly fearsome and accurate ace sniper [who 'never killed anybody'] for the IDF, I came to the conclusion that that was completely in-character for what she did stateside, on the airwaves and in other popular media in these United States. I mean, same thing for Netta Barzilai. Bravissimo.
Until just 2 years ago, it was not compulsory for Haredi Jews. So no.