My website should have some parts that can only be seen when the user is authenticated, some parts that are visibile to everyone.
The forms authentication always redirects the user to the login page no matter what page is visited. Does that mean I should not use forms authentication? How can I solve this issue?
Use <location> element in web.config to set which pages are protected. You need to remove the authorization from the whole web site set it for each protected page in the <location> element.
A common approach is to place all protected pages in a separate folder and specify the location path to that folder.
Another one is to have a class which inherits System.Web.Page and at the Init event to redirect the user to some page, if is not authenticated. Every page should then inherit this page.