Here is a simple test.
what integration you using etc.
Here is a brand new classifieds install and there is no issue I can replicate here
http://www.reeftalk.com/classifieds
Logged in you see this product
login testing
password testing
http://www.reeftalk.com/classifieds/showcat.php?cat=all
Now logged out you see no products
http://www.reeftalk.com/classifieds/showcat.php?cat=all
I need more info about your integration urls to installs etc