Yes and no.
In the past, I used to do something that could be said to be 'mimicking normal people' except that I didn't think that I was mimicking anything, I just thought that I was meeting various odd and inexplicable requirements that the rest of the world put on me.
These days, in many respects very few people would regard me as mimicking normal people. My ability to meet all those requirements fell apart in my adolescence. I am unable to do the things most people would call mimicking normal people. I can't move like them, act like them, etc.
But in one respect, one respect that I hate a good deal and wish I could stop without serious consequences, I absolutely do mimic normal people. And I think this respect makes me different than a lot of autistic people where when they do this it's not mimicking normal people at all.
That's language. Language does not come naturally for me. All the language I have, I have learned through echolalia, pattern recognition, and imitation. I only later (very much later than most autistic people who speak/write) learned to consistently use language to express my inner thoughts and feelings to the extent that it's possible.
But even when I am expressing my inner thoughts and feelings to the extent that it's possible, it still feels incredibly fake. The reason being that my inner life is not just hard to translate into language, but impossible. It's almost the opposite of language -- few to no symbols, ideas, conventional (or many unconventional) thoughts. Those things just aren't there, or not much anyway. My use of language creates the illusion that they are there. As much as learning to use language for my own uses rather than to imitate others has created a great deal of freedom and indeed saved my life, language still feels like death to me. Sometimes it's almost intolerable to run around making people think that all these things exist in my head that are not really there. But I have no alternative -- unlike most autistic people I know, I don't have certain things inside my head at all, so it's not a matter of "translating from my form of thought into language", but rather that using language at all creates a false impression of certain forms of thought that don't exist in me. It's maddening sometimes but I see absolutely no alternative.
And at some point I realized that even though I don't suppress stimming, try to move like most people, or that kind of thing, my use of language is in fact mimicking certain kinds of "normal" thought or even most kinds of "abnormal" thought, either way, mimicking something that isn't me. And as far as I know that can never be changed. As long as I use language, it will create massive illusions in people's heads, and they will relate to those illusions as if they are relating to a person, and believe they are relating to me. Additionally, using language is at least as stressful to me as the constant "pretending to be normal" on a more physical level is to other autistic people, even though I don't "pretend to be normal" in any way other than the use of language. I find it exhausting and need frequent breaks from it. Only when I use no language, and use not even the mental structures that allow language to be used, do I feel like I am expressing myself as I really am. But only when I use language can I hope to communicate a lot of things. It's an unpleasant paradox.
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"In my world it's a place of patterns and feel. In my world it's a haven for what is real. It's my world, nobody can steal it, but people like me, we live in the shadows." -Donna Williams