For privacy considerations, I'd like to be able to set a group permission to view custom profile fields. Then I could set up a Promotion to that group.

There is a modification for v4 if you're using v4.7.x: https://www.sosinvision.com.br/index.php?/file/40-profile-field-per-user-group/

 

Nothing yet for v5 if you're using the beta version.