We have a few, mind you very few, volunteer fire persons who carry radios, AND badges around. Not sure the reasoning on it though since it is not like a fire can see a badge and stop. Because of the good they do for the community I shrug it off. I was issued a pager as a LEO, and I hated it, I "accidentally" turned it off, or the batteries went dead continually while I was off work. One day I went to work and they handed me a case of batteries. After that I made sure I was out of range on my day off.My job is Unarmed hospital security. I can't carry for the 8 hours I am at work. As soon as I clock out and get to the parking lot I take my uniform shirt off and put on a "civilian" shirt and cap. Then my pistol goes on my belt. I have had people see me shopping and, indicating my pistol, ask if I am a security guard. Since I'm off the clock, away from my job site, and not in uniform, nor would I be allowed to have the gun if I was on duty, I tell them "No, I'm not a security guard." Sure, technically I am. But they see the gun and assume that the gun has to do with my job, ie, I must be an armed guard, which I am not. Just as I am not walking around pretending to be a cop I am also not going to give anyone the mistaken impression I am a Armed Security Officer which is regulated in this State. I just tell them No and then continue what I'm doing.
For what it's worth, the gun isn't even necessary for someone to assume you are a cop or security. I am a ham radio operator and often carry a HT (walkie talkie) on my belt. This alone is enough to make a clueless citizen jump to the assumption that you must be an "officer".
Kudos to you for being responsible while OCing, and not letting people get the wrong idea.