No one is burning down anything. But, again, protest has to be inconvenient. And contrary to the claims made by you and Jan, yes, it is actually completely normal (and legal, in most legislatures) for a protest to temporarily "take resources away from others". Roads get closed for protest marches all the time.
But really, what I miss most here is an argument about the actual subject matter. If you are frustrated about the subreddit being closed, you can direct that frustration at the moderators or you can direct it at Reddit. If they didn't implement their API changes, the protest would end, after all.
You seem to be taking it as a given that the moderators are the appropriate target of the frustration and that they should be automatically the one to give in. When Jan asked me - an unrelated party - to refund his Reddit fee, he could've just as well written to Reddit, telling them that he wants his money back because their insistence on overcharging for their API causes this protest and makes reddit less valuable to him. That would've likely done exactly as much to get his money back. But it would actually exert pressure on someone who has a hand in this issue - after all, threatening Reddit's bottom line is what this protest is all about. And given that his business relationship is with Reddit, that's the only party he actually has any real leverage with. So I'm really confused that someone would bend over backwards, logically speaking, to misdirect their frustration this way.
If you want to convince me, at least, that the protest is bad, you have to convince me that the API charges Reddit is implementing are good and justified and that the moderators are wrong to object to them. You won't convince me with arguments about the procedure.
Or to put it another way: In your metaphor, you are assuming that the moderators protesting are the ones who are trying to sink the boat. I'm not convinced of that. To me, they make a pretty convincing case that it's their actions which are trying to keep the boat afloat, by preserving third-party tools that are essential to reddit's operation and the voluntary labor of the moderators. And if the owner of a ship directs it to steer into an iceberg and the crew objects, I'd expect the passengers to back them in it, instead of complaining that they'll be late and how dare they obstruct *my* right to have the ship go wherever I want.
Anyways… as I said, this isn't actually such a dramatic situation. It's just a website being closed for a bit. And if the mods are open to a vote on whether or not to participate in the protest, that seems a perfectly serviceable process to me. People should feel free to vote on that poll however they like. I just wanted to provide some counterweight to the initial call to vote against the protest.