By that logic, verbal bullying shouldn't be stopped
In what context to you mean? Because in the case of schools, the Supreme Court has ruled that they do have the right to curtail free speech that is actively disruptive to the purpose of the school (I.E, the safety and education of its students). Verbal bullying in a school context falls directly under that. However, that has
everything to do with the fact that school administrators are acting in loco parentis (legalese for "in the place of a parent") over a group of minors. This would not apply to the wider world.
If you mean in the adult world, that too is a little complex. There is the Fighting Words Doctrine of limiting free speech, which the WBC has run up against before, has been generally held to narrowly apply to personal speech. So if a WBCer walked directly up to a grieving military family member and told them "your loved one is burning hell for supporting this fag enabling government", they could be arrested (pursuant to local ordinance) because those are words that could spur a reasonable person to punch you in the mouth. If they stand on a street corner outside a military funeral with signs relaying a message to that effect, that's protected because that is a public example of speech. Incidentally, these limits were first defined during the sixties, over Flag Burning and a vest that said "Fuck The Draft".
An argument can be made, and indeed was made by Samuel Alito when the WBC faced the Supremes, that Phelps and Phriends' protest signs rise to the level of fighting words. The rest of the Court, the
current and oft times split down lines of political ideology incarnation of the Supreme Court, disagreed.