‘Team Rei’ refers to the team that believes Shinji is best suited to Rei. This is in contrast to teams Asuka and Misato.
And, while I just hate to say this…Team Rei is obviously the wrong one and anyone loyal really should just switch allegiance.
Now, besides the obvious facts that dictate that Team Asuka is obviously winning…there are also the icky facts. Rei is a clone of his mom. I was debating with myself whether to spoiler that or not…so uh…yeah, the spoiler won.
I think that fact alone is enough to end the discussion, right? Y’know, ignoring the rest.
Now, all that said, this can vary based on the continuity. The Shinji Ikari Raising Project manga basically ends with Team Rei the obvious winner. I think that ANIMA is also, potentially, a Rei victory…though I didn’t finish reading that.
Team Rei is only winning if Asuka didn’t exist.