Your Name (2016)
If this movie doesn't make you cry, you might want to get your brain checked out. Your Name is about two teenagers that don't know each other, but they inexplicably start to switch consciousnesses for short periods of time, bringing them closer to one another for reasons that are learned later on in the film. There is no movie like this in existence, and you should absolutely ignore your perceived distaste for anime to give it a shot.