> Hasn't it been shown that facts don't change people's mind, but (generally) makes them hold tighter to their view?

I think that is a very lazy dismissal of people you don't agree with by characterizing them as irrational.

Actually people can be very rational to in rejecting "facts".

Let's take a look at something that is widely recognized as safe and effective by almost all professionals - vaccines.

First, it turns out many facts actually depend on a long chain of trust. For example, take vaccines. For a vaccine to be safe, you have to trust the safety and efficacy studies. You have the trust the Pharma company did not cheat on the studies. You have the trust the FDA did an adequate job evaluating the data. A similar situation is GMOs where there are a ton of studies demonstrating safety, but in part because of these trust issues (perhaps not helped by industry sponsorship of some of these studies), many people are unconvinced.

Second, even with the facts, tradeoffs and goals matter. The goal of the people evaluating vaccines is population health, and they are willing to accept a certain rate of complications as long as it is significantly lower than the expected rate of complications of the disease itself. Which leads to an interesting situation. If the vaccine rate is low for a human-transmitted disease, it is in your individual best interest to be vaccinated since the risk of acquiring it is relatively high. If the vaccine rate is almost 100%, it may be in your best interest (selfish) to not get vaccinated since you get most of the benefits of vaccination from herd immunity (other people being vaccinated and not transmitting) and none of the risk.

Secondly, even with definition of safety relative to the disease, there are tradeoffs. For example, the lifetime risk of dying of cancer in the US is around 20%. If you had a vaccine that 100% prevented you from getting cancer, but had a 1% risk of immediate death, is it safe? Would you get it? Would you give it to your children?

Another thing that gets ignored is the feeling of agency. People will tolerate more risk if they perceive they are in control versus not being in control. Take for example flying verses driving. Commercial aviation is far safer than driving, but people are more worried about flying than driving. Also, self driving cars. Self driving cars, likely need to be orders of magnitude more safe than driving before people feel more safe relying solely on self-driving. Another example is general anesthesia. The loss of control knowing that you are dependent on someone else to even breathe is very scary, and anesthesia has invested a lot of effort in making that as safe as possible.

Finally, tradeoffs matter. For example, you would likely save thousands of lives a year if you limited all cars' maximum speed to 35 miles per hour, but it would not be a tradeoff that many people would agree with.

So, if you want to convince people, you need to treat them as rational creatures but with perhaps different values and tradeoffs and different priors of trusts. You need to try to meet them where they are and present the evidence with those in mind. That is hard work. Certainly, much harder than writing a list of "facts" and dismissing everyone who then disagrees as irrational.

One thing I have found what works is building relationships and having skin in the game. I have reassured patients and friends about vaccines by sharing with them that my own children and the children of my fellow physicians in my social network were vaccinated. If the people well positioned and equipped to evaluate the evidence are betting the health of their own children on it, it is pretty powerful validation.