If a member of the forum who makes a topic that they feel is important, and relevant to the board where they have posted it discovers shortly after they have made the post that their topic was moved to "off-topic" even when the topic was already creating relevant engagement, is it possible for them to contest it? or are the moderators always correct?
Of course, you can contest it, and I've even seen people contest it by creating a thread in this Meta section of the forum, some will even create it in the Beginners & Help section to make their dissatisfaction known to all. I've also seen at least two members rewriting the same post at where they deem fit to be the relevant section of the forum if the moderator is not cooperating since they are fully sure of what they wrote, especially when everybody reading it knows that it makes sense and was posted at the right section.
Many will even garner more relevance and merits due to that, because at times, it is obvious that the content creator is right but the moderator could be overbearing. Nevertheless, what I can say is that moderators are given power more than regular users, so they can do and undo it. If you protest, some of them might reason with you and do what you want, but I think that some more reputable members and/or their fellow moderators intervene too.
Above all, moderators are also humans, they are bound to make mistakes, and this could be traced to mood and stress at times.