When I'm not sitting at the front playing with the controls, I have been know to do a bit of shooting, long range rifle competitions. I have flown to a fair few competitions in far away places, the procedures vary, but, in general, collecting a firearm straight off the luggage belt is normal. In times past they used to put a big red "FIREARM" tag on the transit case. For reasons unknown the procedure for ammunition seems to vary greatly, some places don't like it in the same case, some don't care. One flight (some years ago) the captain didn't like the idea of the ammo in the same case in the hold as the rifle, so they offloaded it, and made me extract the ammo and bring it as cabin baggage, I kid you not.
I have been known to stand right at the far end of the conveyor, just so the entire flight gets to gawp at it as it slides past.
The reality is, that while seeing it making it's way around the baggage conveyor is odd, once you step through the customs gate, you are out there in the foyer with the rest of the locals who may be carrying handguns, or not, and certainly out in the street a few metres away, it's situation normal. Going into an airport, yes, its a sterile area, coming out, it is not.