They do have the right to their own beliefs, but do they have the right to invade a young man's funeral and wave signs saying they're glad he was beaten to death infront of his mourning family?
Madame Zora is absolutely right, many scholars are examining the translations we have of the Bible, and are finding that in many places it has been translated incorrectly, on purpose, because certain parts didn't fit with the doctrine of the time, or indeed changed because they felt that important things were missed out (or in other words, God in his infinite wisdom forgot to condemn something we don't like, so we'll add it in for him).
However, one message that does not appear to have been altered is that we are to love our enemies. Some people think that's a wishy washy thing, but the Bible points out that by doing so, we will heap burning coals on their head. Essentially, what that suggests is that if someone is behaving like your enemy, and you treat them with love and respect, they end up looking extremely foolish, and will feel that themselves. It's easy to fight with someone whos fighting you. However, when you attack someone and they respond with love, you end up looking like a grand A dork (which, to be honest, Fred Phelps is doing pretty well all on his own).
Homosexuals are the last "permitted" group you can publically attack. If Fred Phelps was out holding up placards saying that all black people deserved to burn in hell, he'd be arrested. Likewise if he was attacking all women, or all disabled people. Chances are, if he could attack any of those groups publically, he would be also. From what I've read about him he seems the sort that has far too much anger and self hatred built up inside him to do anything but attack everyone he can.
My biggest fear is that he and his group will progress from celebrating the deaths of gay people, and start to try to cause those deaths. He would have no problems justifying it to himself and his congregation.