It’s possible to let any user view or post a topic without having to register or log-in. In Discussion Board > Settings > User tab, make sure the ‘Permitted viewer roles’ and ‘Permitted poster roles’ do not have any values selected.
To deselect a role from one of these fields, CTRL click (CMD click on Mac) any highlighted value. This will remove it from the selection.
It is important to note that requiring users to register and log-in is an important way of reducing spam and other unwanted content on your site.