Having a military like ours is a privilage. If we didnt have one then where would our country be in the first place? The nation was born out of fire and blood spilt on behalf of others who either couldnt or shouldnt fight.
You should feel no shame in wearing the uniform. No service man should ever feel that way. All I think you should feel is pride. You put forth more than most anybody in this country to keep us going. I would serve if I could however I am medically unable to enlist (already tried).
As for the guy who you ran into, well everybody is entitled to their own opinions... however he never should have blown up at you or your friends in public like that. I dont agree with his opinion but you should remind yourself that its because of people like you that enable him to have the freedom to have his own opinions.