Try each of the following until the issue is resolved:
  1. Ensure the Targeting & Security settings on the page and template are set for the Everyone role to have View access.
  2. Evaluate the link to ensure it does not contain a reference to AdminPage.asp in the URL.  This may happen if a link was copied while logged in, and then pasted.  This sort of link, containing a reference to AdminPage, will prompt a user to login even if Targeting & Security is set to Everyone. (because the system must validate whether or not the user has the necessary rights to access the AdminPage)