I have (obviously) no experience with trying to shoot down a pesky drone, but I have had military experience with various types of small arms. So here's my armchair analysis FWIW.
If it was possible to get close enough to a drone to use a shotgun, ie a few tens of metres, then I assume that would be ideal and the only hazard would be dead drone components falling onto (presumably) the airfield. The same would be true of a 'less-lethal' munition such as a plastic small arms round, but again the effective range for those is extremely short.
However a more powerful, longer range, weapon would probably have to be a sniper's rifle or similar. This introduces the very real risk of a high velocity round (even one that has first passed through the structure of the drone in a direct hit) ending up several kilometers beyond the intended target. It might be pretty unlikely to hit someone on the ground, but if it did so then it could certainly kill them.
In some parts of the world the habit of 'celebratory gunfire' (eg firing your AK47 into the air to mark your cousin's wedding, or your party getting elected) does frequently end up injuring or killing people several streets away. What goes up must come down.
So I could well understand that a decision to use a military weapon against a drone near an inhabited area would not be contemplated lightly.