It appears it's not possible to hide/show columns via the customization form if said columns aren't marked as AllowMove. It should be possible to add/remove columns from the grid layout regardless of whether those columns can be reordered within that layout, e.g. AllowMove.
Proposed Solution:
Add a new OptionsColumn flag called AllowHide. If this is true, the column may participate in interactions with the Column Chooser/Customization Form.
Ticket
DS53998
Visible to All Users
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The following property has been added:
GridColumn.OptionsColumn.AllowShowHide (bool);