Hmmm. I could see the argument for you not being allowed to have a firearm in a vehicle, not on your person, if the owner of the vehicle (the county) doesn't allow it. For example, you pull up to a gas station and get out to pump gas, leaving the firearm in the vehicle. Remembering that 34-45-103 applies to private vehicles, I could imagine that the owner of the vehicle hasn't authorized you to leave the firearm in the vehicle. That said, I can't see how any government entity in Utah could disallow a permit-holding citizen from carrying a concealed firearm on their person. If you ride a city bus, you can carry the firearm on your person, but you can't leave the firearm on the bus (even if you are the bus driver).
For that matter, unconcealed is also lawful, though I could imagine there could be some difficulties with that one, depending on how the people you would interact with in the course of your job would view the presence of the firearm (for example, presuming you are some sort of sworn officer when you are not). To draw a somewhat silly but still valid example, let's say you are going door-to-door conducting a survey for the county, with two .50 caliber handguns on your belt (and hopefully your belt can hold the >20 lbs). The average person answering the door is going to wonder "what the heck" about the very conspicuous firearms. Now try and ask them questions about the quality of service they are experiencing.
Oh... and I'm not a lawyer and this isn't legal advice.
Dr. Dave (UtahCFP@gmail.com
Utah Concealed Firearm Permit Instructor (CFP Class info at http://www.utahcfp.biz
NRA Basic Pistol Instructor, Basic Rifle Instructor, Basic Shotgun Instructor, and RSO
NRA Life Member
GLOCK Certified Armorer