Mind Reading & Minority Neurology
When it comes to nonverbal communication, NTs are wonderful at "mind reading" by picking up on a lot of little cues from the person they're watching and listening to. A nonverbal communication deficiency is a big part of an autism diagnosis.

"Autistics can't understand other people's minds." True? Or is a general statement better: "People have a hard time understanding minds unlike their own."?

That would make NTs just as impaired as autistics are--when interacting with autistics.

If you're NT, you'll be good at understanding other NTs, not so good at understanding autistics. You might easily make the assumption, "Autistics can't understand other people's minds." I don't think you can really be blamed for that. It's just the effect of being in the majority, and the way people's minds are made to form systems of ideas. You encounter certain combinations of things repeatedly, and out of those you form a general schema that you apply to other similar things afterwards.

If the people you meet have similar minds to yours, you form a schema that starts with your own mind and branches easily out to other minds. As a result you can "read" them very well. So you assume that you can read everyone's mind, because most of your experiences confirm that idea. When you meet an autistic person, you start out by misreading them as though they were typical; then after a little more interaction you start adjusting your schema to include a different variety of human. The problem is that you've had a huge amount of practice with NT minds, but only one experience with an autistic mind; so you are relatively inefficient at this task. To add to the complications, the autistic cannot easily read your mind because he isn't nearly as good at forming schemas as you are, and because his own mind doesn't give him a good example of NT to work from, as yours does.

That "majority effect" is big! The minority naturally has trouble both being understood and understanding, and as a result, the statment, "Autistic people have trouble understanding other people's minds" is true for 149 out of 150 "other people"! It's pretty easy for an NT to form a schema based on that, and it'll be true most of the time. But there's the failing of general schemas: The assumption that "other people" means all other people, rather than most other people, is crucial. It means you attribute the communication error entirely to the autistic, rather than realizing that part of the effect is due to the differences between him and most others.

This is a communication gap that forms when a large majority interacts with isolated members of a small minority.

But there is some truth to the idea that autistic people are worse at mind-reading even between autistics, when the neurology barrier isn't as much in play. Autistic people, on average, focus on detail. That means less schema-formation, and though autistic people do seem to understand each other better than they understand NTs, most (?) of us don't tend to generalize as much as NTs do. So we see individual autistics, and the diversity of the Spectrum, rather than a general "other autistic person". On top of that is the very real diversity of the spectrum--it's harder to generalize from autistic to autistic than from NT to NT, even if you want to do it. And autistic people generally have more experiences with NTs than with other autistic people; so they have their own minds to draw from, but not as many other minds to apply the template to. So you have a person who doesn't generalize too much, doesn't have many similar people to generalize to, and those he does have tend to be more diverse than the ones an NT would have.

Individual autistics may vary. As always.

And of course there are pitfalls to this sort of mind-reading--the dangers of applying a general template to a specific individual are obvious. Too general, and you will misinterpret your subject. You might do so even if your schema isn't very general, if your subject is far enough down the autistic Bell curve. And at the extremes of generalization, you might form a stereotype that could even run to prejudice. So be careful--understanding other autistics better than you understand NTs doesn't mean you understand them perfectly, nor that you can assume that you know what they are feeling or thinking. No one can ever understand another person's mind; he can only understand his own, then extrapolate from that based on new information from the person himself. The more you study your subject, the better you will learn him.

Still, the mind-reading between autistic people is rather striking--not as strong as NT mind-reading, but definitely there.