Question: Ayn Rand mentions in The New Left that some ideas, like some actions, need to be restricted. She has also said that one has the right to express any idea whatsoever. How are these two contradictory ideas resolved? In Ayn Rand's view, would someone have the right to express views that are diametrically opposed to freedom, such as communism?
Answer: Objectivists absolutely hold that we have a right to freedom of speech. It is an aspect of our broader right to liberty: the right to take such actions as each of us judges proper, so long as we do not initiate force against others.
I believe the passage you are referring to occurs in Ayn Rand's essay "The Cashing-in: The Student 'Rebellion." On page 45 of the second revised edition of The New Left (in which that essay appears), she writes: "There can be no such thing as the right to an unrestricted freedom of speech (or of action) on someone else's property."
This is entirely consistent with Rand's defense of freedom of speech. I have the right to decide what speech is proper in my house: I can demand that an offending guest leave the premises. You have the right to freedom of speech on your property and through your property: the articles you write, broadcasts you produce, etc. Because of freedom of speech (based on the right to property) a university may welcome whatever range of ideas it deems appropriate, as may any private organization.
If you want to stage a protest march, don't assume you have a right to use my lawn to do it on. Or my university's lawn, for that matter.
Thus Communists have every bit as much right as any other people to employ private means to promote their ideas. And an audience has every bit as much a right to ignore, blacklist, or boycott ideas they find repugnant.
Rand goes on to argue in "The Cashing In" that state universities should not be bound by constitutional free speech requirements. Her argument is that state institutions undertaking essentially private functions should act as private actors would. I think that as a matter of law Rand is wrong, and that there are good reasons for the state to always be constrained by constitutional limits, no matter what it does. But I agree with Rand on the link between property and freedom of speech, and I think she is very right to emphasize that government should be circumspect when it intrudes on private functions (which, by the by, it should in any case not do).
You can read a recent Objectivist commentary on free speech on campus, "Free Speech and Postmodernism" by Stephen Hicks.