I'm struggling with the same thing and I've been thinking about a possible way to view this.
Over time, people can become used to someone else. On the other hand, Aspies struggle with our external presentation as we have a poorer "theory of mind", at least if that's how the term is supposedly used. Basically, we struggle to understand how someone from the outside is seeing us, so we rapidly change our behavior based on our mood. Most people also change their mood rapidly, but do not change their behavior because they are more in sync with how others are perceiving them and learn from a young age to behave in the same way.
Example: You meet a friend, but on day 1 you are very depressed. You will be flat and cold, but since first impressions count he will think this is how you are permanently. The next time you see him, you might be very happy, and he will see this as an odd behavior. Over time, this gives off a presentation of neuroticism and instability, even if you yourself are a very stable person. This person will distance themselves from you without even knowing they are doing it, and on top of that, the uneasiness this person experiences will be communicated to those around them if you are present using social cues.
So my ultimate tip: Both be aware of how you behave around others, at least to your best ability, and on top of that, don't let what they think about you dictate what you think of yourself. You have to give signals to them that you want to behave a certain way and there's a chance they will listen after you know them more personally.