What Monk Ed said, but also: I assumed that Asuka wasn't on a relationship scale of Toji. Shikinami was "only" a roommate and fellow pilot, not anybody close. So far there's no romantic interest on Shinji's end, but it's not like Shinji completely ignored Asuka either. I think this is where people have misconceptions about the film.
And hell, even with Rei, Shinji is treating the girl similar to NGE!Kaworu where he's mainly interested in Rei for personal reasons (Which is as a means of getting closer to Gendo. With NGE!Kaworu, it's to find solace in another person since everything's going to shit.) despite there being genuine caring. (Stop and think about it: Does Shinji ever really try to get to know NME!Rei or NGE!Kaworu on a personal level?) Yet there obviously is genuine caring, when you remember Shinji is pretty nurturing to Rei, Asuka and Misato in 2.xx with playing the part of caretaker/cooking them meals.