This issue occurs when the Data Protection and Privacy setting is enabled in the org and the Experience Site Contact has an associated Individual record with 'Don't Process' or 'Forget this Individual' flags enabled, which prevents site membership from being established.
A possible cause for this is the org has Data Protection and Privacy enabled, and the Experience Site Contact has an Individual record associated with it that is blocking the ability to make the site user a member of an Experience Site.
Once complete you will need to trigger the adding of the user as a member of the Experience Site. This can be done several ways. Three examples are:
Once membership is re-established you can turn "Don't Process" and " Forget this Individual" back on and the site membership will remain intact.
For more information regarding Data Protection and Privacy please see the following:
Data Protection and Privacy
Also see the following for details on updating membership for your Experience site:
Add Members to Your Experience Cloud Site
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