This is one of those questions where the answer can legitimately range from $0 to well over $100,000 per year, depending entirely on the forum and its business model.
A huge number of forums don't make any money at all, and many aren't even trying to. In those cases, community managers and moderators are often volunteers who contribute because they're passionate about the community.
Then you have the vast middle ground: forums that generate some revenue but not necessarily enough to create substantial profits. For these communities, the focus should be on fair compensation that matches both the workload and the financial reality of the site. A forum bringing in $1,000 per month while spending $950 on hosting, software, and operating costs is in a very different position than a forum generating $10,000 per month with those same expenses.
The business model matters just as much as the revenue. Some forums reinvest nearly everything they earn back into development, infrastructure, and growth. Others are profitable businesses where owners are regularly taking money out of the operation. Those situations naturally create different expectations for staff compensation.
That's why a payment arrangement that feels generous on one forum could be completely unfair on another forum of a similar size. Context matters far more than member counts alone.
Once you get into large commercial communities or corporate-run forums, community management becomes a professional role with standard salaries, benefits, employment laws, and all the responsibilities that come with a traditional job.
So for me, the real answer isn't a specific salary figure. It's that compensation should be fair, sustainable, and aligned with the forum's goals, revenue, and business model. Depending on the situation, anything from a volunteer position to a six-figure salary could be the correct answer.