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This would deny students freedom of speech. It's not their fault if some inbred racist hick finds it offensive.
Not all schools are public entities and thus obligated to let you exercise your freedom of speech in whichever manner you choose.
that is only some schools. The premise is talking about all schools, not only some private schools.
That's not necessarily true. OP is vague.
in public schools, at least in the state of MN, there needs to be a reason to ban the shirts. If the shirt doesn't cause the disruption the shirts can't be banned.
students wearing the clothing with "Black Lives Matter" would cause the disruption in school.
The root of the problem is not #BlackLivesMatter in this case. Most likely, white or non-black students would be causing the disruption, not the wearer of the shirt. If schools gave their students proper education about racism and harassment, classroom disruption could be avoided.
the school locates in South Carolina, where always has racial issues.
In Tinker v. Des Moines, the Supreme Court held that in order to prohibit speech, the school "must be able to show that its action was caused by something more than a mere desire to avoid the discomfort and unpleasantness that always accompany an unpopular viewpoint." Q.E.D.
Freedom of speech? Anyone trying to support peace should not be punished for it.
Political speech is almost always fair game under Free Speech laws.
the shirt is not in itself offensive. It does not say "ONLY black lives matter." It does not say anything negative at all. I don't see why other students would have a problem with the shirt, and unless all clothing with "political" statements is banned under the dress code, there's no reason to ban.