I was mystified by the List feature, as I could sort and filter my lists using any of my fields, but could not include all of the fields in my lists - they just weren't there in the Field List for the columns.
I read a couple of (now locked) old posts of users with similar problems.
Anyhow I tracked down the reason. In administrator/components / com_comprofiler/admin.comprofiler.html.php
at around line 165 you will find
$database->setQuery( "SELECT f.fieldid, f.title, f.name"
. "\nFROM #__comprofiler_fields f"
. "\nWHERE f.published = 1 and f.profile = 1"
So to appear in the list a Field must be published AND in the profile. Sounds reasonable.
But I have lists that are just for Admin use, which need to include details that are not in public profile.
So I just deleted "and f.profile = 1" and hey presto I get all the fields to choose from in my lists.
I hope this helps others ....