There's two types of forum moderators.
Some are paid by the service provider. They offer a commercial service which requires the presence of a moderator to ensure compliance with certain standards e.g. making the place child friendly.
Others are volunteers from within the community the forum supports.
In the former case I might consider the role if I didn't get better money elsewhere. An interest in the community would be at a proffessional level only and any restirctions on my adopting a secondary role as a member of the communty would be entirely in keeping with an employer demanding certain standards of proffessionalism. In such a scenario, if I was drawn into the community and could no longer live with the restrictions of my professional involvement I would have to resign as a moderator.
In the latter case the moderators are drawn from within the community. They are unpaid and simply offering extra time and effort towards the mainenance of a community of which they're an integral part.
Often such moderators refrain from wearing their moderator hat in threads within which they're participating allowing another moderator to take a more impartial viewpoint. I don't think many would be prepared to make the additional sacrifice of being unable to contribute as a forum user in order to contribute as a volunteer moderator. I know I wouldn't.