My experience in running forums began long ago, and continues through a learning period today, but the basics have made themselves clear to me: open discussion and eugenics.
Open discussion involves allowing any topic that is on-topic to be discussed; for example, in a board about soccer, you would not have American football topics, military gear topics, or conservative politics.
However, any submission must be in the correct form — informative, polite, and relevant — so that it contributes to discussion for not just the participants, but most importantly, the readers. This means that obscenity, ethnic slurs, and excessive incoherence can be removed.
This avoids viewpoint discrimination while maintaining quality:
Viewpoint discrimination is a form of content discrimination particularly disfavored by the courts. When the government engages in content discrimination, it is restricting speech on a given subject matter. When it engages in viewpoint discrimination, it is singling out a particular opinion or perspective on that subject matter for treatment unlike that given to other viewpoints.
This means that we remove:
Under this standard, for example, you could not exclude paleoconservative content from a conservative board, or Communist content from a liberal one. Even if someone were advocating breaking the rules of soccer on a soccer board, as long as the argument is well-formed, it stays.
This allows discussion to stay open and quality to stay high. It requires user eugenics, namely removing those who are prone to be incoherent, abusive, off-topic, or antagonistic to the topic. This seems cruel at first, but it allows the minority that is a board to survive the onslaught of outsider users.