Ok, I think this is the root of our disagreement. I think this analogy is flawed. In my mind, what you're suggesting is more like this abused spouse talking about her abusive husband and then going on to say that all husbands are complicit in the violence, she presumes they’re abusing their own wives. Or her abusive husband leads her to condemn the entire instituion of marriage.
No decent human would fail to condemn her husband. And indeed, there are many reasonable arguments about the inherent sexism in the concept of marriage. But this doesn't implicate husbands in general, it implicates the bad husbands and the flaws in the institution.
To go back to King, if you're arguing that saying "let's not judge each other by the colour of our skin" doesn't mean "let's not judge each other for our hateful acts", then I completely agree. King isn't suggesting that we all sing Kumbayah. Good God, he knew better than either of us ever will, how awful racism could be. Racism still exists. Racism must be fought tooth and nail. No argument from me. But in the midst of that, he also saw that judging evil by skin tone was a mistake. Perhaps he saw this precisely BECAUSE of the evils of racism. All it does is keep hatred and distrust (the lifeblood of racism) alive.
As to your point about sexual harrasment. You argue that it would be wrong to bring women into the meeting because it's mostly men who are the harassers. It IS mostly men. But the problem is, your solution ignores the women who are sexually inappropriate (they exist, believe me), and also, isn't it just as unfair to include the men who are innocent as it would be to include the women who are innocent? Should innocent men be implicated simply because they're men, while guilty women are ignored simply because they're women?
In that scenario, my suggestion would be to address the people who had had complaints raised against them, or to speak to everybody about acceptable workplace standards which should be clearly defined. Women don't get held to a differnt standard to men, everybody knows where the lines are, and it's EASIER to complain because nobody can claim they didn't understand the rules.
Of course, this solution doesn't work so well on the scale of a nation and with a problem like racism, but my point is that the standards should be consistent. Black people are asking white people not to judge us by the colour of our skin. How can we refuse to do the same? In his entire speech, King never once condems white people. He condemns A white person (the govenor of Alabama) without generalising to THE "white man". Instead, he condemns injustice. This is our enemy. Making the two synonymous I think can only hurt us.
I'm genuinely trying, I've re-read your comment numerous times, but I just cannot see how you think King isn't arguing against judging people by the colour of their skin. Again, if you're interpreting me saying he thinks "we shouldn't judge by skin colour" as saying he thinks "we shouldn't judge at all" then this is just a misunderstanding. I'm saying (and I believe he's saying) that avoiding judging by skin doesn't prevent us from judging (and fighting) cruelty and injustice. In fact, I think it helps.
Wow, this was longer than I intended too 😅