what content features are on the home page? any custom features on there that might be redirecting?
I would check the settings for each content module to make sure they are not protected though the built in modules should not do any redirecting they would just be filtered out if a user is not in an allowed role
I tried other pages from your site map and they work ok so it seems to be something about the home page specifically. You might try temporarily moving a different page to the home position from Administration > Add/Edit Pages and see if it behaves differently.