If members don't want them in google, tell them to use the profile privacy and make them not viewable by unregistered users. Or, you, as the admin, can make the whole profile page not viewable to google.
Other members can only watch the whole conversation if the profile privacy for visitor messages is set to allow all users to view them. The user can set it so only friends can see them. However, they cannot set it so only the user writing the message can see the conversation - as I said above, if the user wants that then they should use PMs.
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