Rarely are the moderators compensated for their time on forums. They donate their time because of their passion for the subject matter. Although some smaller forums are moderated by the owners, most are volunteers. However, spending personal time as a moderator does build a sense of ownership in how the forum progresses or operates.
Although I do not moderate here, I volunteer my services on other forums. It is up to me to evenly apply the rules and contact those do not follow them. While most forum members understand they are visiting someone else's "home" and need to follow "house rules" to continue to be welcomed, some will try walk line between what they feel is appropriate verses what they agreed to when they joined the forum. People that become a "maintenance headache" for the moderators at some point overstay their welcome regardless off their contributions and it is best they find a forum with rules that are more in line with their views.
No forum member or moderator is irreplaceable and there is no guaranty that everyone will get along. Those that can be civil and respectful to each other are ones you want on the forum (even when they have divergent views), but everyone needs to follow the rules of the forum that creates the baseline structure.