I have a site collection with certain permissions and I want for some people to have access to a folder inside a list (or to an entire list if necessary) without having to authenticate.
Is this possible in SharePoint 2010?
You could, assuming the web application is set up to allow anonymous access. However that might cause a lot of headaches with management of permissions. It might be worth setting up a separate web application geared for anon access to handle that type of content and use PowerShell or content migration to move it from the restricted site to the publishing site.