Does the First Amendment Cover Funerals?

Today the Supreme Court agreed yesterday to hear the case of a marine killed in action, who's funeral was picketed four years ago, with anti-gay protesters bearing signs with slogans like "Thank God for dead soldiers". An article in the San Francisco Chronicle discusses the case and the fact that members of a Kansas church have picketed military funerals to spread their belief that the deaths of soldiers in the war are punishment for our nations tolerance of homosexuality.
In my opinion the First Amendment should not permit protesters to picket private events like funerals or memorial services. Whether or not someone has freedom of speech, they should not be permitted to intrude on events such as funerals with their opinions on the deceased's life or actions.