Selectable

is an option for displayed objects, cells, and notebooks that specifies whether their contents can be selected interactively using the front end.

Details

Even with the setting Selectable->False, an object can be selected as a whole.
With Selectable->False set at the notebook level, no cells in the notebook can be selected.

Examples

Create a cell whose contents cannot be selected:

Wolfram Language code: CellPrint[TextCell["text text text", "Text", Selectable -> False]]

You can select an "unselectable" string, but not a fragment of it:

Wolfram Language code: CellPrint[TextCell[Row[{"text ", Style["text", Red, Selectable -> False], " text"}], "Text"]]

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