You might be right about that, but there's a problem with the alternatives you mention: They would be legal consequences.
Only the legal system can impose a sentence of community service. Anti-hate classes can only be imposed after a finding of wrongful action or behavior.
The whole point here is that the Constitution forbids any government agency from punishing someone for speaking their mind, especially politically. No matter how offensive or heinous the speech is, as long as it does not cross certain hard lines -- treason, incitement to violence, serious threats (as opposed to idle mouthing off), libel/slander, advancement of a crime -- then it is legal and there is nothing the government can do about it, including sending the offenders off to sensitivity classes. And remember, school officials are mostly government employees. They can't do it, either.
Social consequences are the only possible consequences for speech like this. This is protected from government interference. It is left up to society to sort it all out. It does that by social dialogue. In some cases, the dialogue runs along the gist of "Rawr, nigger White House bad, grrr!" versus, "Shut the fuck up, you racist turds." Or in this case, "OMG, check out <Name> being a racist turd."
Sure, we can debate whether the particular reaction of outing them by name and location this way went too far. Personally, I think it did go just one step too far, not because they shouldn't be outed but because they are or may be minors and publishing (or republishing) their identities could be a problem.
But it would be worse, not to mention unconstitutional, to go with punishments such as community service instead.
Did you read my post above about Acceptable Use Policy? Schools absolutely can and do police speech. Students sign an agreement that they won't use computers/phones/etc to do things that break school rules. Then schools can punish students (minors or not) for violating school rules in their text messages, facebook posts, Tweets, Youtube videos, and emails, both on and off campus. And most schools have rules preventing bullying and hate speech. They can prevent students from wearing a t-shirt with a statement on it that offends them, on campus. At the school where I work, a kid reported for Tweeting those things on his own time could be suspended or otherwise lose privileges.