"This is something I learned through thousands of hours of working in this area"? I'd hope that being able to point to concrete achievements would help people to make peace with gaps like this, something that isn't necessarily available to a scientist trying to explain evolution to laymen - since the laymen might not even be able to get what the scientist has accomplished. Most achievements in programming seem easier from the outside so this isn't perfect, but it might be a good starting point.

The thing is that you should just always be sensitive to the possibility of large inferential distances when you're interacting with people of different opinions. "Don't ascribe to malice what may be due to stupidity. Don't presume stupidity when ignorance is as good an explanation. And try not to be too sure your opponent is the ignorant one until you can prove otherwise." That's very much in descending order of importance, but it's always good to keep the third point in mind if you can.