"The relationship does not work" is vague. How does it fail to work precisely? (This can be a useful clue)
There's a lot more in the set up for a privilege set than setting access permission to layouts and fields. A screen shot of the privilege set dialogs might reveal a useful clue.
If Table1::Org = Table2::Org then
The Supervisor and School fields populate correctly with Full Access but not with other Privilege Set.
How are they set to "populate"? are the table 1 fields calculation fields or text fields with an auto-enter field option. Which auto-enter field option have you set up for this? (Looked up value and calculation options can both do this.) Exactly what options did you specify for the method that you used?
If you put the Table2::Supervisor and Table2::School fields directly on this layout, what do you see when you open with a non [full access] privilege set?
Table2::Supervisor and Table2::School are calculation fields.
The Table2::Org which is one stem of the relationship is a Text field. The contents of this field are set by a script.
Placing the two fields on same layout without Full Access privileges are empty; nothing shows in Data Viewer either.
Found the problem!
In Security, there was a way false, very old statement I believe, it limited the viewing of records in the other table. Took it out and now all is functioning.