Summary: Profile fields in Views were either not showing up at all or showing up multiple times.
Solution: Add one relationship to the view for each profile type from Profile2.

I was creating an author profile block earlier this week, but could not get the profile fields to display correctly. Some were empty. After going through field permissions again and again and a load of Googling, I put it in the too hard basket. Yesterday, I was working on a list of users and ran into another weird problem: profile fields were duplicated and in some cases being displayed four times. I thought it might have been solved with aggregation or choosing to display only distinct entries, but that didn’t work.

It turns out the problem was with the relationships. You need to create a unique relationship for each profile type. I had one relationship mapping multiple profile types (to get access to different fields from different profiles).

The solution to this issue  was found here at Drupal.org. It is also outlined in the Profile2 documentation.