Conflicts of interest are not resolved by voting or in a popularity contest. A moderator with a conflict of interest should withdraw from that role or refrain from acting in situations/discussions where his or her conflicting interests come into play.
If a candidate for moderator has conflicting interests, a prior step to being elected should be to declare them publicly. Then we would all know in which discussions their work as moderator might be problematic.
It is not a question of doubting anyone’s honesty. It is about ensuring fair play in discussions. If I were acting as moderator, I would be the first to remove myself where my impartiality could be doubted.