I can't reproduce this bug. I think you were either standing too close to the door and actually clicking it, or there was a pressure plate or tripwire and the fishing rod was activating that.

Where was the door you tested on?


ty @VivienLeigh for halping

 

• Cannot reproduce with an unlocked door in a town.
• Cannot reproduce with an unlocked door in the wild.
• Cannot reproduce with a locked door in a town from the distance, but it opens properly when right-clicked while standing next to it.*
  
• Cannot reproduce with a locked door in the wild from the distance, but it opens properly when right-clicked while standing next to it.*

*This right-click behavior has ceased to function with empty hands or other blocks/tools at some point between 1.8 and 1.10.