The thing is, what speech signifies and what impact it has varies according to the context in which it is communicated. The medium is part of the speech (McLuhan's famous quote "The medium is the message") and you understand the speech differently depending on that medium (McLuhan's book "The Medium is the Massage"--this was originally a typo by the printer, but McLuhan decided to keep it). The WBC can have God Hates Fags as their website all they want, but that's just not going to have the same impact as it will when it's expressed at a funeral, and thus that context (website vs funeral) is part of the speech, and so is (or should be, at least) protected.
How is the context of the speech part of the speech? Yes it effects it, but that doesn't mean it's part of it. The color of a room can effect how a painting looks, but that doesn't mean the color of the room is part of that painting.
Again, if a kid wants to express his/her hatred of homosexuality at school, they must say it at an appropriate time and in an appropriate manner. Going around harassing other gay students is speech, and it has more of an impact, but he/she doesn't have the right to it because it's actually harming others. WBC can go as far as they want, but they can't actually harm others. By harm, I don't mean offense, I mean actually psychological harm. The limit of speech, in my opinon, begins when the speech entirely depends on the negative reaction of others (at that point I don't consider it speech either, since speech has to have some independence anyways).
Speech expresses an idea. If the idea expressed changes, the speech must in some way have changed.
Having a website called God Hates Fags expresses that you think that God hates homosexuals and want the world to see it.
Going to a funeral and saying "God hates fags" expresses the idea that not only does God hate homosexuals, but that this hatred is in some way linked to the funeral, which is different than what the website expresses, and, as intended, it provokes a much more negative reaction in others (something that a statement on said website saying "God hates fags and caused/allowed/etc someone to kill twenty children in Newtown, Connecticut to show it" doesn't, at least not as strong a reaction).
You can't divorce the speech from the context in which it's made because the context in which it's made changes the meaning. The medium is an intrinsic part of the message and it makes the message affect us in a different way (ie it massages you into viewing the message differently).