One of the founding principles of this country is “no taxation without representation.” Disregarding the will of the voters seems to run contrary to that.
If you ask people if they support a constitutional right to free speech, they'll probably say yes. If you ask them if someone should have a right to say some specific disagreeable thing, many people will say no.
Similarly with NIMBYism, people say they want houses built and support candidates who say they'll fix the housing crisis, but if you ask them about some specific planned development close to them, they say no.
I have no idea what the will of the voters actually is on this issue. Everyone agrees there's a problem, but most people are against all solutions.
Source? I think most people are going to understand that speech you disagree with is part of freedom of speech.
Is Fred Phelps holding a sign saying "Fags die, God laughs" at a military funeral protected speech? It was non-obvious enough that it went to the Supreme Court, meaning a lot of people thought he had no right to say that.
Do you have the right to burn a US flag in protest? There literally were laws banning that until the Supreme Court said that's protected.
I don't think it'd be hard to find people who are still in favor of a flag burning ban, or who want to ban offensive speech near funerals.
I don't have statistics but anyone who was around for those examples knows there were plenty of people on both sides.