Freedom of speech is protected in the First Amendment to the US Constitution:
Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the Government for a redress of grievances.
The First Amendment was originally intended to restrict the power of national government and was spurred by experience of a particuarly repressive English law of the time (which made criticising the government a crime).
The Supreme Court has made some exceptions (obscenity, incitement to violence, defamation etc) but the kind of English law I cited earlier in the thread would probably be struck down (at least in part) as unconstitutional.
I think people may question why things can't be done to stop this kind of behaviour
Distasteful as picketing funerals may be, there is no law against it as long as it is done peacefully - and in the most recent Supreme Court ruling it was pointed out that the a-holes were 1000 yards from the funeral.
IANAL (in either jurisdiction) and my sympathies lie with the bereaved.