I've never had any success there. I don't know that it can be done. What are you going to tell them to convince them that these are problems they have, or that they are problems? It might be different if they are young people, but in my experience, past a certain age, if that's who you are now, that's who you will always be.
Once again, this is fruitless. Anybody that knows how to think critically does. Those that don't, don't because they can't. Most often, they don't even know what the phrase means.
Furthermore, critical thinking is a skill that only comes after years of university. I don't see it anywhere else. You don't have to go to university to be intelligent, but if you want to evaluate evidence properly and arrive at sound conclusions, you need to learn a lot of rules, and you need to learn them over years of practice. What fraction of people can construct a sound argument, or identify the fallacies in an unsound one, and what fraction of those have no advanced formal education?
We see plenty of people on these threads that do that quite competently, you included, but to the best of my knowledge, they are all college graduates. They go to Sunday school and learn the creation story through repetition and exhortation. Then, they go to university and take a class in biological evolution. Nobody says, "Today, we'll apply critical thinking." They are simply given the evidence available to Darwin and others since along the with arguments that lead to their conclusions, and see how it's done without the phrase ever being mentioned. Then they take a history class, then a math class, then an English literature class, and in each case, they will be presented facts, evidence (perhaps examples), arguments, and their conclusions, and by repeating this way of thinking over and again, they eventually learn the skill to a greater or lesser degree. I am quite sure that by the time I finished my education, I couldn't define the term critical thinking, although I was already doing it to some degree and with some success.
But it was only in the last few years here on RF that I have come to understand that most posters not only are unpracticed at critical thinking and can't make a sound argument, but also that large numbers don't know what it is or what it can do. This is manifest as, "That's only your opinion" when they see it. In fact, isn't that what Dunning-Kruger is all about. It refers to, "people with limited knowledge or competence in a given intellectual or social domain greatly overestimate their own knowledge or competence in that domain relative to objective criteria or to the performance of their peers or of people in general," but I would suggest it is better described as underestimating the skills of others, a subtle distinction. That is, where I once thought that most people had at least an idea of what critical thinking is whether they had developed that skill in themselves or not, and that they respected it in others and hoped to do well at it themselves, that is not the case at all. When an anti-vaxxer takes advice from a crackpot rather than the consensus of recognized experts ("What does Fauci know about it anyway - he's just in it a big pharma's behest"), it's because he doesn't know that the opinions of the two are derived using different methods. He is unaware that there are other methods of determining what is true.
So, from that perspective, how do you persuade others to think critically? In the last third of life, you don't. You can't even teach them what it is, much less how to do it. The best one can hope for is to help them learn who to trust, and even that seems futile. I was thinking about this last night while watching the new and hearing about 140 Republicans signing a document repudiating the opinion of the RNC. I thought that that might reach some Republican voters in a way that the January 6th committee never could, since the latter is definitely not trusted. But teach them to think critically? That ship has sailed.