He cries when he has a reason to cry, which is a lot, because tons of bad shit happens to him, which, if you were a tramatized 14 year old boy, you would cry about, too. Name ONE instance where you wouldn't have cried when he did. Stop kidding yourself.
And turning down ass? Stop being a preteen. When did anyone offer him sex? Never. MAYBE Misato that once.
All of these generic complaints about Shinji have no credibility, because they come off as being the same "LOL, if I were Shinji, I woulda fucked her!" comments you hear from ten year olds who watch the show, kidding themselves into thinking they would do any different.