The mosque isn't even a debate except by fear-mongering media moguls who want to distract attention away from their massive Saudi contributors. (See Rupert Murdoch's contribution lists.) As far as WBC, the 1st Amendment exists specifically for those crackpots. The majority of the US thinks these guys are nuts, however the majority does NOT have the right to dominate the minority. In the case of WBC, what they do is distasteful, but no different from mainstream conservative groups like the Tea Party or even anti-abortion activists at clinics. These two groups have more following, however, so we tend to delineate between their methods and those of small extremist groups like WBC. The same goes for any political group, liberal, conservative, religious or areligious--any of them. The more followers, the easier it is for us to accept their "right" to whatever they choose to say or do so long as it isn't obviously hurting anyone. It's human nature.
The framers of the 1st Amendment knew this, so they created a means of protecting small, distasteful groups from the majority (whoever that may be). In the case of WBC, they're typically a decent distance from the funerary party, not screaming in their faces. In some cases, the families wouldn't even know the people were there except for advance warning or for seeing it later on the news. There is no violation of law (half of them are lawyers--they make their money suing people, so they're careful to know all local rules and regs), so they've the right to spew their nonsense as they please. If they were in someone's face, literally, or using racial epithets or some other hate speech, it'd be different. As it stands, they espouse a known opinion in an unpopular manner.