(For the sake of abstract curiosity:)

If that holds for unintentionally bumping into someone, or spilling coffee on their shoe, then as a logical extension it holds true for things I say, whatever medium I use to say them.

I would apologise for spilling coffee on someone but not in this situation. The analogy is not a good one and definitely not one of logical deduction! Some relevant factors:

• Astro was being obnoxious and disrespectful. (Barring a couple of exceptions that would not apply in this case) apologising to people when they are being obnoxious and disrespectful legitimises people behaving that way to you.
• This isn't direct personal interaction going on in good faith. It's an absurd public spectacle. It's an entirely different situation and one in which people's judgement changes drastically, losing perspective. An apology here wouldn't just be
• Give an inch and they'll take a mile. See JGWeissman's behaviour here with Constant for an illustration. An apology would be twisted into a confession of guilt. As though Dfranke actually did something wrong. (Apart from spam the forum with Qualia nonsense - I'd appreciate an apology for that!)
• Dfranke didn't call Astro a dude - it was a guess that it was even one distinct individual and picking an arbitrary gender for the hypothesised individual isn't saying anything about Astro at all. In fact the unknown downvoter could just as easily have been me. My voting patterns (everything by Dfranke in this thread down whenever I noticed it) match exactly what he described.
• Dfranke apologising would be a (minor) slight to all those who have defended him from perceived unjust accusations. The clear consensus (by voting pattern) is that Astro was behaving inappropriately and there was a solid base of support for Dfranke at least as far as pronoun use goes. You don't undermine that without good reason.
• Dfranke basically isn't involved in this discussion. That's a good way to be. Some people have taken it as an excuse to push their spivak related political agenda but he has chosen not to try to desperately justify himself. Staying uninvolved is a wise move and if he did choose to make a statement it would be significant primarily as a political feature, not an instrument of furthering interpersonal harmony.
• If Dfranke did feel guilt (or, more realistically given that it would be a response to public criticism, shame) then that is a problem of miscalibrated emotions and not something to submit to. Guilt would not be serving him in this instance and he has the opportunity to release that feeling and move the stimulus response pattern (disapproval -> shame -> supplication) one step closer to extinction.
• Even if an apology is met with approval in the moment it is not necessarily producing an overall good outcome for you. It may get an apparently encouraging response from a minority but would not lead to being treated with respect in the future either by those people doing the encouraging or by others. You apologise when you have actually done something wrong, not because someone else tries to emotionally bully you.