The post below mentions efforts that states have adopted to limit the ability of Pastor Fred Phelps and his family to disturb the solemnity of funerals--especially military ones.
The pastor believes that American soldiers in Iraq died because of God's condemnation of the acceptance of homosexuality in the United States. He makes his case known, loudly, as close as he can get to the funeral services.
Considering that this is not just free speech, but the free expression of religious belief (let's assume his opinions are sincere), the Constitution seems to be on his side. The Supreme Court may decide that the greater interest of society in preserving the dignity of funeral services is more important than individual free speech and free expression, but then again it may not.
There is no right to dignified funerals guaranteed in the Constitution.
He may be labelled a public nuisance, or argued to be causing public disruptions that undermine public order, but that can apply to many other public events as well, and may justify an expansion of governmental authority beyond what is prudent.
Is Pastor Phelps another price we pay for living in a free society?
The First Amendment Center Weighs in on the topic here.
Here's a news item about a Kansas law against funeral picketing.
Shirley Phelps explains the picketing.