I've never known a woman who cared that much about height. However, many are turned off by guys who are constantly worried about their girlfriends being taller than them. No woman wants to have to slouch all the time to avoid hurting her date's ego.
It seems like a lot of guys around here narrow down the field of women they consider appropriate for a relationship quite a bit, and then complain that they can't find anyone. I realize that some people don't find certain heights, hair colors, or whatever attractive, but if that's not the immediate issue, you're eliminating a lot of potential partners for no good reason.
Successful relationships, at least any I've ever been in, don't start with people saying, "I want one with brown hair, big boobs, and between five foot three and five foot six." They start with people who bump into each other by chance, or meet at school or work, or share some kind of activity they're interested in, and then get to talking and realizing they have something in common. I met my husband at a game of Scrabble held in our college dorm on a night that everyone had been snowed in. I almost didn't go to it at all; I certainly wasn't going to find a boyfriend. I'm socially awkward at best, but I gave it a go, and lo and behold someone actually talked with me.
Talk to people, pay a little attention to the things you do that are misinterpreted most in first encounters, and these things will more than likely come with time. Maybe you'll never date a supermodel, or the one girl that you have a crush on. Maybe the girl you never notice because she's just kind of quiet and average is the one who will like you for you and not give a rat's ass that you're an aspie. Maybe you'll never know because you were too worried about the pursuit of the dream date to take the time to talk to her.
Not all women are hung up on finding a tall, dark, and handsome guy with an expensive car. Maybe most women your age are; that's a possibility. But I don't know any who are actually dating or married to a guy like that. Women may date men for those superficial reasons, the shallower of us may marry them for such reasons, but no one actually loves a guy because he's tall. A woman loves a guy for the way he treats her, for his sense of humor, for his idealism, for his intellect, for his talents, for his passions, for his endearing foibles. A woman loves a man because she can look at him and talk to him and see that she'll be happy doing that same thing in the future. If what you want is just meaningless contact, then yes, appearance and whatnot is the big deal-breaker. But if you actually want someone to love you, want someone to be in a lasting relationship, then you're paying attention to the wrong things.