An evangelical explained this behaviour to me, and I'm wondering if he was correct.

Evangelizing is a requirement of their faith - if they fail to evangelize they are in trouble with G-d. G-d does not want them to "convert" people - all He cares about is them going out and evangelizing. Apparently, constant rejection "immunizes" evangelicals against rejection. Once they are fully immunized, they are able to tune-out the world around them, and hear only the word of G-d.

Evangelizing cleanses the mind which enables G-d to take full possession. Once that happens, evangelicals cannot see, hear, feel, or sense anyone but G-d.

In our community, evangelical families were known for children with serious problems, including drug, alcohol and porn addiction, severe depression and anger issues. Apparently, evangelical parents really are tuning-out their own children.