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I can't never ship Shinji with Rei due to the incest factor. The argument I always hear is:
>Rei is Shinji's half-sister since she's a a combination of Yui and Linith
Yeah, I get that. If we take the religious symbolism into the mix, Abram married his half-sister, Sari, and God approved of it. But Shinji always saw Rei more as a sister he needed to protect rather than someone he can romantically get intimate with. Of course, Rei 2 wanted to have some form relations with Shinji as shown before she self-destructed in her Eva.
Their relationship could work, go ahead and ship them, but I personally can't especially since Rei 3 doesn't show any form of interest towards Shinji.