As someone who knows a lot of trump supporters and trump haters, this is what people who are afraid of trump need to recognize. I've seen the advice from this article work first hand, and I've seen people who don't understand what the author is talking about make situations worse first hand.
Interesting. Maybe give some examples?
It's hard work, but what I've found to work is this: Instead of getting into an argument, state what you believe and talk with them in terms of cooperatively finding out what claim is correct. Don't let your ego get in the way. Figure out what exact parts of the claim they believe (or disbelieve), and research those specific parts, with them present. For example, say someone doesn't believe in global warming. Maybe they just don't believe in anthropogenic global warming, or they misunderstand some of the evidence. Shouting that they're stupid (which I've done before, it's about as ineffective and childish as it sounds) won't work, because you aren't addressing their actual concerns, which they themselves might not be fully aware of.
This is slow, hard work, but it does pay off. You have to keep an open mind, and be 100% aware of your own behavior. If you are dismissive because of a value difference between you and the other persons cultural background, it's counter productive. Likewise, if you can't admit when you're wrong, then it doesn't work either. Admit when you don't know something, and that you are flawed and imperfect like everyone else. Take this as an opportunity to learn about your own beliefs.
A concrete example: A close friend believes some conspiracy theories (no AGW, moonlanding faked, etc.) I've successfully gotten him to go from the position of "Global warming is a liberal conspiracy" to "Climate change is a real and serious issue, but I'm not 100% on the evidence for it being man-made". This has been really hard work over a period of about a year, but it's worth it. I'm not done, but this is how it's gone so far. Any time he expresses his opinion about this, I'll express that I disagree. This usually leads to some anger on his part because people tend to get their opinions wrapped up in their identity and take disagreement as a personal attack. I 'll point that out if things get too heated. Instead of just saying "no" or "you're wrong", I'll say something like, "well let's find out. I could be wrong." A lot of times, he won't believe the research I pull up, or pull up a denier website. I go through the denier websites and investigate claims point by point. For example, quotes from people who have since changed their mind, cherry picked lines from studies, things like that. Most of the time, it didn't seem like there was any progress made that session, but the next time it came up, his opinion would be a little more nuanced, or his opinion would move a little away from the conspiracy.
It's slow, gradual work, but we are both more educated on many issues because of this. I feel the important thing is to treat their opinion as valid. Often when you investigate why people believe irrational things, you find that they believe them for rational reasons. People they respect believe that, they have personal experience that runs counter to the research, they distrust the source of the claim.
If you don't understand why someone believes something, you can't change their mind about it.
/rant
Sorry for the wall of text, this is something I deal with all the time. tl;dr: Change people's minds one person, one opinion at a time. Be patient and open minded. Research it with them, and make sure you are cooperating, not verbally fighting for dominance. Changing someone's mind is an incremental process. Emphasize being open minded and doing research instead of advocating "not believing crazy things".