Aspies usually pass the Sally-Anne test, however eye-tracking has shown that many do so by logic rather than intution. I've never done an eye tracking test, though I suspect I would pass it. The reason is that I do intuitively impute thoughts/feelings in others, I just don't impute different ones than my own.
For as long as I can remember, I would empathize with other people's pain; if a friend got hurt I would feel their pain too. When lining up for vaccinations at school, I couldn't watch the kids ahead of me get their shots because I would cringe when the needle went into their arm. Even with this ability to empathize, I still had significant social problems since my adolescence.
How does empathy work?
Until recently, I thought empathy worked by figuratively putting yourself in someone else's shoes, and feeling what you would feel if you experienced the same thing. In other words, I thought it was a matter of perspective taking, and feeding the other person's experience through your own brain. So as long as your emotional response to a situation matches the other person's, your intuition of their feeling would be correct. Since I seem to lack or have significantly impaired social emotions like shame and deference to authority, it follows that I can't impute those emotions in others. Considering how debilitating emotions like shame and social anxiety can be, I consider myself fortunate that I'm not burdened with those emotions the way many NTs are!
While having a discussion with wife 2.0, I learned that there can be more to empathy than putting yourself in someone else's shoes. I found out that she can impute feelings in others that she wouldn't feel herself in the same situation, something I suspect is common in neuro-typicals. This means having a set of rules in your brain not just for your own emotions, but also for other people's emotions as well. It would explain why I had few social problems with some people - people who's emotional responses to the world are similar to mine. But for people with different emotional responses, there is more likely to be issues.
I've disussed before how other people's emotional responses can be learned. When I separated from the ex, learning about social dynamics and flirting was helpful for dating. While it didn't significantly improve my batting average (I'll never be a lady killer), it did improve my understanding of my interactions with women.
Many times I've heard that people on the spectrum need to learn social skills so they can better interact with NTs. But shouldn't NT's have to learn too? I find NTs tend to be wrong about my feelings more often than I'm wrong (or miss) their feelings. Some people have even tried to tell me that I should change my behavior so NT's are less likely to mis-perceive my actions. When it's the NTs jumping to the wrong conclusion, the solution is not to get the Aspies to change their "unpredicable" behavior, the NTs need to learn to make better predictions.
After wife 2.0 read Loving Someone with Asperger's Syndrome, she said it seems the non-Aspie partner has to make most of the changes in order for the relationship to work. While that may be true, I think it would be more accurate to say the non-Aspie partner has the most to learn. And at least for me, I'm not looking for my partner to change; I'm happy that she doesn't try to change me. Love you MEJ!