Being able to tell when someone is not interested in learning is a vital skill in resisting oppression, I think. I have a system now. If you make a problematic statement, I will
Step 1) give you some information and some criticism to see how you react. If you react with defensiveness or repeating yourself, the conversation is done: you're displaying a desire to 'win' an argument, not to learn (and I skip to step 3 or 4, depends on my energy level).
Step 2) If you respond with questions and/or new statements, the jury is still out and I will still engage. If you appear to rearrange your thinking in some way as the conversation goes, I will continue to engage unless/until you seem unable to absorb a key piece of information.
Step 3) I will offer you some resources for self-education and ask you to stop talking to me on the subject until you do your homework. If you try to argue with me after that without doing your homework,
Step 4) I'll tell you that your opinions are useless and give you a warning to stop engaging with me.
Step 5) Ignore my statement of being done with the conversation and I will stop you with a block/ban.
If I'm having this discussion on someone else's page, I will stop at 3, and usually reconsider if I want to have this person connected to me. If I'm having it in person, then if I get to 4 or 5 I will just tell them I am no longer interested in talking with them, and leave (either physically or mentally).
I've had a few drive-by comments on my post on the importance of labels. The first one immediately revealed that they weren't interested in learning, by calling it bigoted and intolerant to require people to acknowledge privilege. Them, I just laughed at and told to go away (instant step 4). Another stranger responded with an argument that by labeling themselves, oppressed peoples are the source of their own mistreatment. This I engaged with more seriously, explaining that they don't understand oppression and telling them the true source of oppression (step 1 and part of 3). They then told me no, they're correct, etc, which revealed that they weren't interested in learning. So then I laughed at them and told them to go away (step 4).
If at any point, someone comes to me with a request for resources to learn, I will courteously and generously try to come up with the resources I think would be most helpful. I will give of my time, energy, and thought to do this. But I will not waste any time on someone who just wants to try to verbally fence with me. Pripois often find it entertaining to fight about social issues that have no negative effect on them, and I have no interest in providing their entertainment. (pripoi= privilege-poisoned person, one who denies privilege and/or refuses to try to reduce its effects)
I consider it a radical and important action to tell a privileged person that their opinion on oppression is useless. They are almost always shocked by this, and it sticks in their memory. Being flat-out told you are wrong and uninterestingly so is a rare experience for pripois. It encourages them to self-examine. I know this was true for me when I was privilege-poisoned. (I am still privileged of course, but no longer to the point of denying my own privilege or refusing to attempt to ameliorate its effects)
On realizing that I'm wrong, I often feel embarrassed if I think I should have figured it out already, but I also feel happy because it means I learned something new. I prefer to realize things myself because that's less embarrassing but I feel grateful when someone tells me information that makes me realize I was wrong about something with a lot of impact, because it feels like the world is suddenly profoundly changed and I have potential for many new understandings. It's a gift to have someone correct my misunderstanding -- yes, even if it's done rudely. Also, one of the habits I have built as a protection against embarrassment is to say, "yeah, I was wrong" as soon as I realize it. It prevents me getting defensive, and it allows me to stop calculating the extent of my wrongness and focus on figuring out a way to do better. It sort of short-circuits the shame cycle, for me. (if it is something I feel really bad about, I can fret about it later where the person confronting me doesn't have to deal with my self-centered guilt/shame)
How not to be a pripoi: an example.
An example of reducing the effects of privilege would be: you're a man and you're hanging out with a woman and a man. The man makes a sexist comment and the woman responds explaining the problem. You resisting oppression and reducing privilege effect would be saying something like "I agree" or "you need to listen to this" rather than making your own argument in the same vein. Men have the privilege of having their arguments taken seriously while women are ignored, and you can push back against this by being supportive without adding your own voice, if there is already someone who is not a man speaking. If no one else speaks up, then by all means, express your issue with the sexist comment. But if after your initial statement, someone who actually experiences that oppression takes up the discussion, remember that it's time to pull back and be supportive.
I learned that^ method by example, when a default (white hetero cisgender nondisabled male) posted a really sexist article and myself and three women had pointed out various issues in it. The default ignored all of our arguments. Then an ally who is a really great person (also a default) came in and said something that was a rephrasing of one of the same points. The pripoi default then suddenly acknowledged that point, while criticizing the rest of us. This was a fail of allyship because it allowed the pripoi to dismiss 90% of what we had said, and when I noticed it I realized that I have done the same thing before with issues where I am the ally (such as racism or mobility impairment). I determined that I would do my best to express only support in a discussion of an issue that doesn't affect me when others have it handled. However I have a shit memory and I know I have fucked up since then, so if you ever notice me failing on this please call me out.