My recommendation would be to put Content Controls anywhere you want to be able to edit the contents and then apply document protection for forms. The real question is how to identify the 'white' cells. A 'white' cell could have no fill or a white fill via indexed color or RGB specification. It could also have color on a background or foreground setting so you might need to fiddle with this to identify target cells correctly.
The following code works on my test tables and shows how you could step through the code to help identify cells and add the CCs to the found cells.
Code:
Sub SelectivelyAddCCs()
Dim aCell As Cell, aCC As ContentControl, aTable As Table
For Each aTable In ActiveDocument.Tables
For Each aCell In aTable.Range.Cells
aCell.Range.Select
Debug.Print aCell.Shading.BackgroundPatternColorIndex
If aCell.Shading.BackgroundPatternColorIndex = 0 Then
If aCell.Range.ContentControls.Count = 0 Then
ActiveDocument.ContentControls.Add Type:=wdContentControlText, Range:=aCell.Range
End If
End If
Next aCell
Next aTable
End Sub
Once you have added the CCs you can turn on the Restrict Editing for forms (via the Developer Tab). You will be able to find code on this forum to do this but you can easily record this step to see sample code.