Some of the research I've done using questions similar to those asked on the exit poll revealed a similar issue. Somewhere I saw an explanation that many evangelicals do not like to be included in a category that usually includes fundamentalists. Many of my students who would be in the evangelical category also resist any type of label beyond "Christian." Students regularly tell me that their church is nondenominational, but it really is evangelical.
Sounds plausible to me, but has this come up in other polls?
Update: Here's an alternative explanation from a commenter:
Myy sense of this is quite different. While it's true that many evangelicals want to avoid being lumped as "fundamentalist," it's equally true that "Protestant" has become a stand-in for more liberal mainline denominations and that evangelicals have a stake in avoiding identification with that group as well. The "Other Christian" self-identification, I think, is an attempt to avoid being lumped with the more liberal "Protestant" category.