As explained in your other topic what you are trying to do you can not do without CB Conditional. It is the only plugin that can condition off this as it can condition against the HTML output of the avatar field. This is done with the below conditional.
Display: Field conditional self
Field: Custom > Value
Value: [cb:userfield field="avatar" /]
Translate Value: No
Operator: Equal To
Value: (leave empty)
Translate Value: No
Mode: Show
The issue you were hitting with your other topic below is you wanted to condition the field multiple times, which you can not do as CB Conditional does not have AND/OR conditioning at this time. In short you need to compromise on what you're wanting as the functionality just isn't there to 100% provide what you want.
www.joomlapolis.com/forum/255-developer-members-support/231695-5600-use-the-request-connection-javascript-link-for-other-uses?start=36#273812
There is absolutely no other solution for what you're wanting besides coding a plugin to do it.
CB Privacy does not and will not hide PHP values. PHP values are what substitution if conditions check against. This means the substitution if usage will see a value even if you've hidden it with CB Privacy.