I have no idea what NTR is, as someone who is not primarily a speedrunner of 3ds games.
It destroys the framerate and stuff like that. It would be SUPER easy to cheat. If I was a mod, it wouldn´t be allowed.
It should be allowed, anyone who actually reviews their speedrun should be taking a look on it. All NTR viewing does is stream the gameplay, the framerate is limited due to the limitations of the 3ds (30-45fps generally, you'll never get a higher framerate with the software because the 3ds just doesn't have enough power to provide 60fps through wireless) and it is also very easy to tell if they are cheating during an actual run.
In no form or shape does it give you an advantage (This isn't like Nintendon't or emulators). It's just a way to stream the footage, and it does provide a good enough image to see clearly what is going on.
I would trust it over a photo-shopped image or an image you can barely even see. Considering all this, you can net a consistent 30fps which is acceptable. If a video posted looked very chopped otherwise, just reject it due to poor quality.
Its all game by game case, I know for some titles it just doesn't work (Mario Kart 7) due to all the loading screen differences. Though what I've learned and seen is that this is generally fine for anything that uses IGT.
Personally, I think banning everything can be stupid. I personally just throw time penalties on things instead or I use a time "limit" you can get with it and going beyond on wouldn't be allowed. Otherwise all you are doing is shrinking down your own community and preventing them from even trying to get into anything if its their only solution. This is 2018, most people just stream attempts and love the appeal they get with it and many people would love to see actual runs from 3ds games.
People look too deeply into these things and seriously, for the 3ds? I think it should be lighten up with what I suggested not just with this game but others.
EDIT: @blueYOSHI I want to add that I did talk to Cosmo about NTR and what it can do. For now, it is accepted for this game.