Wearing issued kit isn't the problem(unless its stolen an isn't supposed to be owned by civvies).
Wearing qualification badges, unit insignia, etc is what pisses people off since guys an girls had to go through courses an combat to earn those badges like Jump Wings, Combat Infantryman Badge, Ranger tab, etc. You may think you are respecting the troops who wear those badges an immatation is the best form of flattery(or whatever).. well that don't work for wearing badges, etc you haven't earned. To the troops who earned those badges its disrespectful to think you have the right to wear them an show them off for a airsoft game(or whatever), etc. Go to places like
www.socnetcentral.com/vb/ http://www.usparatroopers.org www.army.ca and ask them what they think about guys wearing SEAL Trident's, Ranger an SF Tabs, Airborne wings, etc
None of that stuff is needed for airsoft, you can go for a certain look without using those badges.
Wearing badges for Reenacting/Living History is a bit of a different subject though.