If you have a site enabled with anonymous access and if you drop this web part on a page. you will notice that this webpart shows the contents to anonymous user correctly however when you click on any of the list item(hyperlink), It will challenge you to enter windows credentials or you will get "403" forbidden error.
After examines I found that Content Query Webpart usages copyutil.aspx page in layouts folder which in turn redirects to appropriate edit form depending on the type of the list. That's where the problem lies.
The "CopyUtil" class inherits from a generic class called "UnsecuredLayoutsPageBase". This class has a property called AllowAnonymousAccess . Which the inheriting class should override and set it to the true or false based on how web application is configured

Workaround:
1) Override the ContentQuery Web Part's XSLT and instead of using copyutils.aspx use the "dispform.aspx"
2) Create a cusotm copyutil.aspx page and override the AllowAnonymous property