When replacing a cast fishing rod in your inventory with another fishing rod (with the same NBT data), then the fishing rod shown in your hand in first person might be displayed as if it is not cast.
- Place two fishing rods next to each other in your hotbar
- Cast one
- Scroll to the other
- Place one fishing rod in your hotbar and another one anywhere else
- Cast the fishing rod in your hotbar
- Open your inventory
- Hover over the other fishing rod and press the hotbar key of the first one (e.g. if it is in slot 1, press 1)