IMO the argument that we shouldn't criticize online AH threads because they're not professional and so criticizing them isn't fair falls apart given that we are also in the online AH community. If you post a story in the online AH community it's fair for online AH people to criticize you for it. I do however think there are three criteria that make an online AH story worth criticizing (I'll use Queen Nixon as an example of each criteria because this thread has talked about it to death):
1. It's intended as a more or less finished piece: I think a lot of published authors in this thread are coming in with the assumption that if you post a story on an online forum it's clearly intended as a first draft, but that doesn't really hold up when talking about stuff on AH.com and the like. I would say that most content on AH.com is intended as mostly finished, and Queen Nixon is a good example of that. The author clearly intends this to be the final (or close to final) version of the story. I agree that we shouldn't be attacking first draft as the "worst thing ever", but finished pieces are fair game.
2. It's popular and prominent: Sturgeon's Law says that 90% of everything is crap, but from a reviewing perspective most crap isn't that worth commenting upon. Who cares about a story that only 3 people (including the author's mother) have read? However, popular works are inherently worth talking about. For instance, Queen Nixon was at one point one of the most popular works on the forum, generated a ton of discussion, and was nominated for a Turtledove. This is as close as an unpublished AH work can get to being a bestseller, and as members of the community it's fair of us to offer our perspective.
3. The author has decided to ignore constructive criticism: All writers make mistakes, and the best way to get a writer to improve is to offer constructive criticism. "This is shit" isn't at all useful, and if that's all an author hears they're not going to improve their craft and may even be driven away. However, some authors refuse to listen to constructive criticism. The author of Queen Nixon basically declared that anyone who offered criticisms of his work were trolls and that they should fuck off. At that point further constructive criticism is useless, and so going "Well actually here's all the reasons this is complete shit" is the only way to criticize a work. I understand the idea of simply ignoring works you don't like, and this thread has definitely talked about works like Queen Nixon far more than is warranted, but I also think that there's nothing wrong with really harshly criticizing terrible works from time to time. As long as you aren't spending too much time obsessing about bad works it's fine and actually pretty fun to pick apart the flaws of terrible media.