When we enable anonymous access for a site and want to search list items as anonymous user. There is a site collection feature called “Limited-access user permission lockdown mode” which prevents list items to be indexed as anonymous access.
A List item will be viewed through DispForm application page like below: Lists/AverageRatingStore/DispForm.aspx?ID=1.
Above feature stops anonymous user to access application pages. once you deactivate the feature and give a crawl, anonymous user should be able to search list items.
Thanks,
Prasanta
Prasanta Barik 