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I'm sorry but I don't know what you mean by that. Do you mean adding a link in the main menu for visitors to access the Jomsocial section of the site before being logged into the account? This site is meant for the staff and parent of a child nursery, they are very concerned about their privacy so a visitor who isn't a member can't just go into the site.
Just out of curiosity why would not having a "home entry link" in the menu cause the avatar uploader not to work? This isn't working for users who are signing up for their account and for users who are already logged into their account. Regular image uploading works for a users adding photos to their posts it's only when the upload pop-up box show the uploader isn't working.
this is about joomla technical issue when using SEF URL.
at main menu item I saw there is Parent that linking to jomsocial frontpage. could you please activate that menu item?
with that, all jomsocial pages will using that menu item ID
for more better explanation, please read:
documentation.jomsocial.com/wiki/Toolbar_Explained
What toolbar is used for, Component Entry Page section