When hecklers drown out or silence a speaker, it's known as a "heckler's veto," a term coined ironically by a professor at the University of Chicago.
In a strict legal sense (and in fact), the Heckler's Veto is when the government suppresses the speaker because of the possibility of a violent reaction by hecklers or a violent reaction by the crowd incited by the hecklers. It is the government that vetoes the speech, because of the reaction of the heckler. Under the First Amendment, this kind of heckler's veto is explicitly unconstitutional. In US case law the rulings regarding the heckler's veto is somewhat mixed, but most findings say that the speaker's actions cannot be pre-emptively stopped due to fear of heckling by the hecklers, but when faced with imminent violence authorities can force the speaker to cease their action in order to satisfy the hecklers. But that doesn't mean the hecklers can't be arrested and prosecuted for a wide variety of charges, including disturbing the peace, inciting violence, and for conspiracy.
Most people would agree that vocal protests outside a speaking venue, and quiet protest (leaflets, for example, or holding up signs) inside, are fine, but draw the line at interrupting speakers. Such behavior is not only incredibly rude, it is intolerable. Freedom of speech is among the most fundamental, and among the most cherished, of the bedrock values our nation is built upon. A great nation, free and independent, depends utterly on the free exchange of ideas. It is absolutely critical. This is non-negotiable. Those who attempt to suppress the rights of others violate core principles that are the foundation of any free society. The layman's heckler's veto is little more than verbal terrorism, and reeks of gross intolerance.
We cannot allow such behavior. In fact, the more strongly you disagree with an idea, the more strongly you should protect its display. Otherwise, all it takes is for someone louder or more powerful than you to disagree with what you have to say. Protests about controversial subjects is part of our culture and part of our foundation. But so is being a place and culture where all points of view can be expressed and heard. There are ways to protest that respects free speech and allows people with opposing views to be heard. Being rude to a speaker, drowning out and attempting to silencing opposing ideas is not among of them.