I am a high functioning autistic person and INFJ.
I think the key here that people miss about empathy is that what most people are doing is not *really* empathy. They just put themselves into another's shoes, more or less sucessfully, and measure their empathy level on their enthusiasm for doing so rather than whether their imagination gives them a correct answer or not. That's how you get people claiming to be highly empathetic with animals who think a dog in distress is smiling or that a tense, skittish cat is in need of some cuddles. That also extends to people who's life experiences are vastly different to theirs, like not fully grasping the extent to which early trauma affects personality development or the psychological impact of poverty (demonstrated clearly with the penal system btw)
Similarily, the autistic brain is also different. I can't tell you how many times people tried to get empathetic with me by putting themselves in my shoes and spectacularly failing at correctly understanding what I feel (made worse by their insistence that they are correct). The opposite case was also frequently true. The issue is that the "actor" who you put into my shoes is nothing like me because my brain is different to your experience. Living in a neurotypical society, I had many "corrective experiences" on that account. Most people didn't.
That said, I consider myself a highly empathetic person. I learned to observe people and support my "feelings" with concrete findings. I don't put myself in other people's shoes the way I was taught empathy works. I observe how they are actually feeling without imposing, which is actually more natural to me. Some even called me psychic for that when I was more open about it. I yearn for connection and do my best to make others feel better. One way my autism comes into the mix is my utter confusion on how to apply social expectations to the mix, though. Say, I've met a guy who was missing his hand. He was very non-challant about it and made constant jokes about the fact. I noticed the frayed edges of that presentation right away, though. An anxiety, determination to not be vulnerable, a fight for self-worth. I wished to connect to him, make him feel like everything's fine and make sure to get him understand that he's an amazing human being (which I was sure of after spending a few days in his company). I failed to understand how to do that without breaking through boudaries set up by his mask, though. Another time I was talking with a girl I knew. She talked about how happy she's with her boyfriend and how great it is since they moved in together. She projected a happy, confident persona, but I noticed a pattern of fear and unease at the edges. My thought was that he's abusive. I was rather certain. I later turned out to be right. But I didn't know how to get close enough for that discussion to be appropriate since we weren't close. I was so confused that I hid in the bathroom, actually. I felt that there's something that needs to be addressed, but there literally is no template how to breach the surface and dive into what's real. And I couldn't continue with the interaction on the surface level. Social rules make people happy, but they're also a tools to hide the real things behind ritual and masks. That's incredibly confusing.
I think the trouble with typing autistics is that you're trying to determine the personality of a cat living in a world of dogs. The behavior of the cat will not be true to it's personality in that environment because it's pressured to cope and conform with something alien to it. I don't think that this "adjusted" personality has much weight, rather one should look inward to understand their inner workings instead of relying on performance in such a case. For example if I lived in a world of people of the same neurotype, I would struggle significantly less with connection and my unique way of understanding the world would not be discounted (and not force me to adopt a meachanically sound "thinking" strategy that I could demonstrate).
This is really interesting and helpful. I hope you stick around and share more perspectives.