To enable public profile for anyone, you need to first assign the attendee role to the contact.
Go to Contacts. Click on Reviewers tab. See screenshot.
Click on a Reviewer's name, assign the attendee role and click on Save.
The public profile option is now being displayed. Enable it.
If you want to enable public profile for multiple reviewers at once, do the following:
Go to Reviewers tab.
Select all reviewers in the list.
Click on Bulk Edit button (hover on Actions). See screenshot.
Select Assign Roles from the dropdown and enable Attendee role.
Click on Save. This would assign the attendee role to all of the selected reviewers.
Now, select the reviewers again, click on the Bulk Edit button, select Public profile settings from the dropdown and enable public profile for selected reviewers. See screenshot.