The backfire effect is obviously not universal, otherwise it would be impossible to teach for example Newtonian physics. So if you present strong enough proof people will change their minds.

I think the problem is that people don't really learn what a strong proof is, so when two people who each have a weak understanding of the topic tries to argue both will see that the other is ignorant but not that themselves are ignorant. After the discussion both will have correctly refuted a lot of claims from the other side, thus "strengthening" their own views. If this often happen to you then you are likely not as well informed as you think you are.

In short, I believe that "you can't reason someone into a position that you didn't reason yourself into" is true, while the popular "you can't reason someone out of a position that they didn't reason themselves into" is wrong.