> ... but you can't reason someone out of a position that they didn't reason themselves into.
I'm living proof that this isn't true. I was a Young Earth Creationist for nearly 30 years, despite having an engineering degree from one of the world's best universities. I no longer believe in anything supernatural. It took a very long time, but I was eventually reasoned out of a position I wasn't reasoned into.
When people incorporate ideology into their identity, challenging the ideology directly is often interpreted as a personal attack or something else not worth honestly engaging with. A far better approach is to examine the methods people use to reach conclusions. There's a conversation technique called Street Epistemology that does exactly that. IMHO, it's the most productive way to have these kind of conversions.
This has become something of a hobby horse of mine over the last few years. I was raised as a fundamentalist, so I had a lot of anti-science indoctrination to get over, both explicit and implicit.
The main problem with this sort of thing, including the methods outlined in the article, is getting past the backfire effect. The best way around that seems to be challenging the methods used to come to a belief, rather than challenging the belief directly.
There's a technique called "street epistemology", loosely based on the Socratic method, that's specifically designed to avoid the backfire effect. See https://streetepistemology.com for more details, or https://youtu.be/v9utXKpFxCo for a great example of it in action.