When a list's permission is set to allow anonymous users to view it, all
users are able to view the contents of the list. 
The only catch to viewing a list as an anonymous viewer is that if a
user has an avatar attached to their
profile, as an anonymous viewer, you will NOT be able to view their avatar without having first signed in. 

In this article, we will show you how to add an avatar to a user's profile, and then how
to configure a list so that anonymous viewers are able to view an avatar without the Windows Security dialog box appearing and requiring them to sign in.

How
to use avatars for users in a list

For this example, I have created a Discussion Board list which has posts by users that have photos
attached to their profiles.

After creating the thread and replies, you will see that
each user's Account name has a place for an avatar next to it.  If the
user has not yet attached a photo to their profile, the avatar will appear as a grayed out silhouette.

To edit a user's picture, you will need to go to System Account and click on About Me.

In the About Me section,
you are able to edit your profile to
include an image of yourself that will appear for users when they view a list
to which you have posted.

How
to specify anonymous access for a list

To begin, navigate to the Security section under Central
Administration and click on Specify
authentication providers.

Under Edit Authentication,
check the box next to Enable anonymous
access.

Next, go to your site and under Site Settings, select Site
Permissions. Click on the Anonymous
Access menu on the Ribbon.  From there,
select the Entire Web site radio
button.

After completing the steps above, go to your site. When
you do this using Anonymous permission, you will see the Windows Security dialog box appear without a user photo displayed,
as pictured below.

How
to configure a list to be able to view an avatar

Before you begin your configuration, make sure that you are
logged into your site via a System
Account.  You will need the
permissions associated with the System
Account in order to be able to publish User
Photos for all users.

Next, expand the arrow next to the Account Name.  From there, select
Site Settings.

Go to Site
Permissions and click on the Anonymous
Access icon on the Ribbon.  On the Anonymous Access screen, select the Entire Web site radio button.

To set the appropriate Anonymous permission, go to the User Photos list from your Site
Settings menu.  Please be aware that BEFORE
you edit a picture for a given user, the User
Photos will be shown on the Site
Contents.

After you have finished editing the picture for the
user, the User Photos will be hidden
on the Site Contents.

To access the user images, you will need to run the following
URL: http://servername/my/User%20Photos/

Once you have done this, go to the Library tab and select Library
Settings.

From the User
Photos Settings menu, click on the Permissions
for this picture library link.

Click on the Stop
Inheriting Permissions button from the Ribbon.

From the Permissions tab, click on the Anonymous Access button.  From there, select the View Items checkbox and click OK.

When you return to your site using Anonymous access, you will be able to see a user's avatar without the Windows Security dialog box prompting you to sign in.