>>4065377It does seem like he tried to befriend her near the end of the series, before he realized Rei's nature --- we see them talking by the train station in one of the last episodes. After her death and resurrection he seemed scared of her because of her nature, and during EoE at least, they disagree about what is the best state of mankind. I haven't read the manga so I don't know how different the relationship is there, but I've heard it's more developed, but also similar to EoE. I also haven't watched the series in a couple of years, so I am sure some nuance has escaped me.
But yeah, Shinji is an idiot in numerous respects.