Military members both current and former: Would you think it rude if someone approached you and thanked you for being in the military?

Just tonight, I saw a man in army fatigues in the grocery store. Whenever I see a member of the military in fatigues or a uniform, I have the urge to go up to that person and thank him/her for serving. I was going to approach this man until it occurred to me that maybe he would find it strange and unsettling.

So, military Jellies, would it be acceptable for me to do this?