I saw a post on #kataradeservedbetter where they talked about certain Kat@angers or Zutara antis giggling about Katara threatening Zuko in the Western Air Temple, like: "hahaha, she would totally kill him, she hated him so much", but agreeing with Aang that it would devastate Katara if she had killed Yon Rha.
This is something I noticed as well, and I agree with @oxyintelligent and the anon who asked them: Those people are just Aang stans who like Katara as a love interest for him, but nothing more. What is fine in general, but not if they claim to be Katara stans who have the best interest of this character at heart.
She was threatening Zuko in order to protect Aang, so when her intentions are Aang-focused it is totally fine. Though, facing her mother's killer, who caused her severe trauma, and MAYBE killing him is something completely different. Why? Because Aang said so. This is neither Aang-focused nor -approved.
And, of course, Katara was also listening to Aang when she spared Yon Rha because she can't make decisions on her own, it is either evil Zuko or good Aang (so, the men) who have an influence on her.
And telling Aang very clearly that she'll never forgive Yon Rha doesn't matter to them. No, they say something like: "I'm sure she did forgive him, anyway." Not only that. Suddenly what Zuko says—who is soooo evil, mind you—counts: that violence wasn't what she needed. Because, you know, as strange as his comment is, especially right after Katara indeed has been violent towards the leader of the Southern Raiders (and showed no regret): he said that Aang was right. Again: Aang-focused or -approved.
It is also very telling that I haven't seen ONE Zutara shipper who claimed that Katara should forgive Zuko, even though it would go against the ship if she didn't. And not one who couldn't understand her righteous anger towards him until she forgave him right after their field trip. Don't say there aren't any, it is just very telling how many Zutara antis I've seen doing so in comparison. And this is another thing: Would she have forgiven Zuko falling in his arms out of gratefulness if his intentions really were that selfish and dark? Again, those people don't listen to her.