How can guests post in a forum? is a question which comes up fairly regularly so I thought I would post a suggestion with the above title in the hope Mr Google and community members might get to it in future.
The simple answer is: guests cannot post in forums, even though you can edit permissions to allow them to. It does not work. However, that is not very helpful if your organisation has a course open to guests and you would like visitors who are not a part of your Moodle to contribute to a forum. Perhaps you have a open course with examples of a new study programme and you want prospective clients to ask questions, for example?
A workaround is to create a new role, the Forum poster role and to give this role to one account which you create uniquely for the purpose of allowing visitors to post in forums in your guest access course. The role is quite restricted; the user cannot change the name or password and can only post in forums, not do quizzes, add to wikis and other logged-in user activities.
Because guests can see the course immediately, they might get confused about how to join in a forum discussion. A label at the top of the page giving details of the user account (username/password) would be helpful. One thing to bear in mind of course, is that, if several people contribute to a forum, their contributions will all come from Moodle Visitor (or whatever you call the account you use) and so it might be an idea to suggest they add their names when posting. On the other hand, it is handy for people wishing to speak anonymously!