Yes, they have to right to say what they please about public issues in public places.
But when they say false things about individuals, they should also have the expectation of being sued for slander and libel, for harassment, for verbal assault, and for emotional distress.
I don't understand why everyone seems to want to make this a First Amendment issue when I see it as far more of a personal issue.
We have freedom of speech, but with that freedom comes a great deal of responsibility.
We cannot say whatever we want and expect others to accept it without question. When we protest something, we have to be sure we are protesting in the right venues so the right people hear what we say. It makes no sense whatever to protest America's gender ethics at a grade school spelling bee, it makes less sense to protest those policies at the funeral of someone who died protecting those ethical choices.
It is not freedom of speech to taunt someone else, then claim First Amendment protection for those taunts.
Bullying is not protected speech.
Claiming to speak for deities is foolish at best, and is protected only up to the point just before those speakers use their speech to bully those who have no connection to those false prophets and their claims. Once the false prophets verbally and textually assault individuals, they have abandoned their First Amendment rights.
It is tolerable (not acceptable, mind you, but tolerable) for someone or for a group to say "My God Hates (fill in the blank)." It is not tolerable or acceptable for that person or group to claim, "God Hates (fill in the blank)" because God transcends one small group of people, and no small group of people can claim to speak for God, only for their God, a Being who is evidently as petty and small-minded as the group claiming to speak for Him/Her.
I don't condone exerting violence against these people who abuse their First Amendment rights. What I recommend for people who use their First Amendment rights to bully others is complete and total media silence. Don't advertise their itinerary, don't cover their protests, don't interview their people, don't publish photos of them. I know the media feels this is Big News and gains wide readership, but I feel they are doing their reading public a disservice by sensationalizing this type of protestor, and by this, I mean a protestor whose apparent goal is to disparage, tear down, and destroy others to get their way rather than to empower positive changes and create stronger community/national bonds through pointing out weaknesses with ways to strengthen those areas.
Look to the protests in Wisconsin for an example of exercising First Amendment rights in a positive and powerful way. Then compare that protest to the vicious, spiteful attacks of the bullies.
We have the freedom of speech, and with it comes the responsibility to refrain from bullying through slander, libel, false witnessing, harassment, and impersonating a deity.