One thing that should be done is a user setting to configure this capability. If it is disabled then their copying to clipboard does not have any effect (this is not detectable by the web page), except if you push the key combinations (or menu items) to normally do so while the text is selected in which case only that text is copied to the clipboard. This also would affect which text can be selected, too, not only the clipboard. Disabling fonts also can be possible, etc.

(On my computer I usually disable the scripts so that it will not do such a things, but even if scripts are enabled, you might want to configure that feature too.)