When you truly reach a point of total apathy regarding how others see you—then nothing you do will be awkward.

Really, I probably could have posted just this sentence. Exactly what I meant.

At first, this attitude was difficult to achieve, and sort of forced - thus I'd go to the grocery store with messy hair, and have to force myself to remember "you're a robot!" Now, however, it doesn't even enter my head to worry.

Although one thing I still kind of struggle with is feelings about the opposite sex. I'm hoping to read more comments regarding it.

This is probably largely what spurred the "robot approach." In my all my favorite fantasy or sci-fi stories, there's always that episode or chapter where A Female seduces all the normal characters (unintentionally or otherwise)... but The Robot remains immune. It's almost like a superpower (in this context), to be unmoved by beauty.

In real life, of course, I have only rarely been approached by beautiful females intent upon seducing me in order to take over my spaceship. But I did often feel like they had undue power over me; so I'd think to myself "ha, ha; she thinks I have a crush on her because she's pretty and I'm not, but really all I care about is science!" (Though I did eventually meet a girl who had a thing for mad scientists. Took more than two decades, though.)

Also, I... uh... once pretended to be gay. Turns out females can be great friends if there's no sexual tension. This served as a valuable lesson to me; since most of the tension was evidently just in my head (girls don't actually seem to immediately assume I'm trying to get in their pants like I feared), if you just act unconcerned you'll probably find they have no problem hanging out with you.

(I just realized a lot of this is not directly relevant to your problem, but it's at least somewhat related, so I've posted it anyway.)