More advise for Aspies:
A possible reason that men with high-functioning Asperger's Syndrome (often nicknamed "Aspies") get accused of being a sexual pervert of some kind, is that it actually seems maybe reasonable to men who are tending to be bullies ... since the bully thinks in terms of potential assault ... and it makes juicy gossip that tends to keep the women away from the Aspie men, the women believing the gossip might be true and are "protecting their children from the assaults of the Aspie." Clever trick, very fitting of bullies.
The reasoning is that men who grow up being bullies are very focused on other people, and are ever striving to be high up in the social hierarchy, making them key deciders of what goes on and attractive to women who want to be on good terms with the bosses.
The Aspies, however, due to their mental wiring, are largely unaware of the social hierarchy and who is boss of whom. So when the boss is going jerk on the social chain so as to make something happen, the Aspie not only tends to fall out of the pattern where he had been blending in best possible to survive, but also the Aspies uncannily are where they see the dirty tricks the bullies have pulled although usually do not fully comprehend it all, but do find the energy going on attractive, the Aspie ever trying to join in on the fun going on but just don't get it, those invisible social rules playing out.
The bully-bosses realize that their hierarchy of intimidation is not for sure going to keep the Aspie's mouth shut, and represents a danger to the boss, or so the boss thinks. Thus the need to "spread the word" that the Aspie is a sexual pervert, don't trust him with anything, don't believe the liar. This tends to isolate the Aspie even more from those he needs to be among, especially needing a woman like other men do, but also to help with those social dealings so necessary to life. So the Aspie is often at least looking at the attractive women, thus the top bosses of the social hierarchy can't count on the woman and the Aspie not getting together some time especially if the boss is putting the screws too hard on the woman. While the bullies cannot admit that they ae not the "best" in the eyes of all women, so it is easier to think that since the Aspies are not obedient in the social hierarchy of intimidation, that they might be "perverts" ready to assault women and children. That is also because the bully mind reign of virtual intimidation is based on threat of assault, projects that the Aspie is similarly thinking of who can assault whom too, just like the bully does.
But the reality is that the bully is far more focused on "assault" than the Aspies are. An Aspie might reflexively lash out at what seems to be in process of harming him, but otherwise is not interested in assault. And that is part of the Aspie's problem, in that people thinking he assaults women and children is totally impossible. Only when the backwash of too many social events does the triangulation center on the probability the Aspie is being called a sexual pervert and danger to women and children, weird as that seems to the Aspie. However, the vast majority of people are not Aspies; and thus are compelled to be in lock-step with the social hierarchy web in which they live, it is how they know how to conduct their doings with others, by knowing whom is boss of whom, who is better than whom.
When the news tells of some hidden assault on a woman or a kid, and the quest is on for who-done-it, if they have seen a bully likely having done it they dare not mention that because the bully's penalty to them will be terrible. So it is easier to finger an Aspie in gossip, and use all means especially if the law enforcement and store security networks can be tricked to get in on the fun of bullying an Aspie in any way possible, thus easing the minds of the population, got their eye on that Aspie and so all is well. If something happens and the Aspie goes down, all breathe a sigh of relief, justice has been served. No matter if the assault on the victim was done by the bullies so as to blame it on the Aspie, to get leverage on the high-functioning Aspie who tends to be far too smart for the bosses to trust.
Although I cannot offer any solution to the Aspies out there regarding coping with this kind of problem, I can say that a lot of top-notch men who were Aspies have been brought down by the bully-instigated gossip this cunningly ruthless way; so if you suspect you are targeted, you are in good company. Anyway, being aware of a possible problem, is a step toward dealing with it better, at least knowing what might be going on. Just because you know it is utterly untrue about you, won't protect you from the gossip-fanned fury of the mob, when the bullies are having their revenge "outsmarting you."
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