I think I managed to replicate the behaviour you describe(On both Firefox and Chrome), and also manage to narrow down the behaviour for it, thus also concluding habits that would reduce the risk of encountering this behaviour.
NPC/Monster Compendium Drag-n-drop behaviour (5E at least)
For open character sheets, their drag-n-drop zone is larger than the open sheet itself. This causes trouble if you have sheets open on the map and want to drag-n-drop NPCs to the table, without accidentally overwriting one of the open sheets.
1. The whole map area below an opened character sheet act as a drag-n-drop "zone", preventing drop to the map.
2. The drag-n-drop "zone" covers the map below the open sheet even when the sheet is open so small that the sheet itself can't act as a drag-n-drop "zone".
3. The map area above the open sheet is not part of the drag-n-drop "zone".
4. Minimized character sheets don't have a drag-n-drop "zone".
So I'd say the drag-n-drop "zone" of open character sheets should be reduced to only cover the open sheet, and not the whole area below it, as it is now.
Habits to avoid overriding characters when drag-n-drop NPCs from compendium
1. If you have multiple character sheets open on the map, and tend to drag-n-drop NPCs to the map somewhat often, it's best to have a habit of keeping the open character sheets toward the bottom and left side of the map, to reduce the risk for dropping npc stats onto an open sheet.
2. drag-n-drop NPCs only to the top right corner, where you shouldn't have any open sheets.
3. minimizes sheets when possible(with a double-click), as they won't be overwritten like other open sheets.
4. Keep some or all open sheets in separate windows. Apparently popped out sheets are still having a drag-n-drop zone on the map even if the sheet isn't on the map. Thanks to The Aaron for pointing this out.
Sidenote
Isn't it much more common to drag-n-drop NPCs directly to the map and
make a new character, rather than overwriting existing ones?
Is
overwriting existing characters primarily used for quickly stat out NPCs
that might only have a name at the start, so if Bob the Burglar is a
npc that only have a name and some GM notes and the players end up
fighting Bob, you'd just quickly drag-n-drop the "Thug" statblock on top
of Bob and it would be ready to go. Or is there some other application
of overwriting existing characters that I don't see?