By making your vBulletin forum private you will prevent guest visitors from browsing and seeing the forum posts.
You can change the access permissions for the Unregistered / Not Logged users from your vBulletin admin control panel->Forums & Moderators -> View Permissions.
You should also alter them in your vBulletin admin control panel->Usergroups->Usergroup Manager->Unregistered / Not Logged In->Go.
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