It is possible. You'll have to manage space specific permission. There is this guide here that can instruct you on how to do that: https://confluence.atlassian.com/display/DOC/Setting+Up+Public+Access
"The relevant space permissions. If you want a space to be publicly accessible, the anonymous user must have at least the 'View Space' permission. To set space permissions, choose Browse > Space Admin > Permissions."
I hope that gives you a hint
You must enable Global Anonymous Access and then ensure the spaces you desire public to grant Anonymous Users View Permissions.
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