Can people who oppose a speaker's message use their 'freedom of speech' to drown out the offending words?
This is called a “heckler’s veto.” The problem with it is that, far from advancing understanding, it inhibits it. Freedom of speech was guaranteed in the First Amendment so that a full range of ideas would be available on matters of public interest. The Supreme Court's interpretation of the First Amendment as it pertains to public college campuses over the past 80-90 years is derived in part from J.S. Mill’s essay, “On Liberty,” in which he asserted that:
“… the peculiar evil of silencing the expression of an opinion is, that it is robbing the human race; posterity as well as the existing generation; those who dissent from the opinion, still more than those who hold it. If the opinion is right, they are deprived of the opportunity of exchanging error for truth: if wrong, they lose, what is almost as great a benefit, the clearer perception and livelier impression of truth, produced by its collision with error.”
Students are not allowed to drown out the lectures of a professor in the classroom without disciplinary action because doing so disrupts the school’s academic purpose. Guest speakers are allowed on campus in order to offer different and broader perspectives, thereby addressing the school’s purpose. So student speech that would drown out a controversial guest therefore can be prohibited.
However, institutions ideally will not simply silence students wishing to protest against a campus speaker. They may restrict student protesters to an appropriate forum, thus allowing both exercises of free speech to occur.