Okay man, I'll give you a real answer. I'm not autistic, but I do know a thing or two about making mistakes without realizing it.
I think the best single thing you can do is truly remain humble and cautious about yourself, your words, and your actions. All of the most egregious mistakes that people, autistic or not, make are based around prideful arrogance. If you stop and observe without prejudice, meaning you take in your setting and try to learn all you can about where you are and what you should do, your odds of making 'autistic' social faux pas will go down. Furthermore, making a simple mistake and then course-correcting, will be more successful than if you were to go on for a long time without realizing. Nobody can expect perfection from anyone, autistic or not, but if you try I think you can achieve much more than you may realize.
I'll give you an example. There's this guy at my work who I suspect is autistic, and he is a pain to work with. We have a TV in our office that about 6 share. Our boss tolerates us having a TV but would be quick to take it away if it created embarrassment or was too distracting. When we turn it on, which is not always, it is usually on the local news or something vaguely professional like that. We have been known to have football on occasionally. During our shared lunch break hour, sometimes we watch more unprofessional shows or movies, but we try to wrap it up around the time lunch of over.
Then this guy joins our office and he just wants to play all kinds of movies and stuff on Netflix. He seems oblivious to how this looks for the people who may come in and out of our office throughout the day, including superiors. Especially being new and supposedly in training, to see him sitting there fully engrossed in watching movies on our big screen.. like a kid who is oblivious to his surroundings. When we confronted him about it he got all defensive and pointed out examples of other people watching 'unprofessional' things, which was usually either lunch break or maybe a slow Friday afternoon when the boss left early. He just doesn't understand any rules that aren't black and white. Anything that requires conditions is beyond him. So it got to a point where we had to just leave it off when he's around.
Another related incident was about him coming back late from lunch chronically. While we get an hour for lunch, some people drag their feet and come in a little late. This is tolerated if the person is a good worker and gets everything done, and is fully trained. But if you're new, you're expected to be available training, and then proving yourself, before we'll tolerate much slacking off at work. But just because he sees someone coming back 15 minutes late, he thinks he can too. I told him we needed him to be available, and he just got all defensive, 'that's not fair!' like a kid. So now when he's around, all of us have to take a strict 1 hour lunch.
As you can see in those two examples, this one individual's inability to perceive rules of situational awareness and moderation, required us to make strict black-and-white rules. This results in a us having a less chill working environment, and us all feeling more stressed when he's around, and relieved when he's not. Thank God he's transferring out soon. Don't be that guy.