It's understandable that the public would be quite perturbed in regards to the amount of days GD has been given off, especially due to the fact that he's not only a celebrity, but a well known one. Idols and celebs in general are already looked down on to a certain extent when they enter the military because they most of the time can opt for "special treatment" in being moved to more secluded barracks and the like to avoid issues among those serving and to "protect them" in essence. Most idols don't want this seclusion, but sometimes it is a necessity. Other times, it's requested and if probable cause is met they are transfered around.
I can see, too, how it can appear that he is slacking/using the military as a time to instead get R&R from his music and performing career - getting foot surgery because he has time to get the surgery and heal from it (whereas if he was actively promoting he wouldn't be able to while recovering etc), but, it's not to say he purposely did this, just that it can definitely appear this way to many and I can understand if people are reading it that way and develop negative feelings because of it.
You are also correct in Korea being strict in how they serve/when they serve etc, and their pride for serving their nation. It's kind of something that many of the current and elder generation (and some of the newer generation, though, this from what I have read and heard from those born and raised in South Korea is starting to fall a bit more by the wayside and "old way of thinking" to an extent) have indoctrinated into them from birth, so to have someone seemingly get special treatment, especially a celebrity - again, I can understand the hostility, unfortunately.