You're right, it's obscene that a privately run conference should have any right to interfere with what potential speakers are able to say in front of their audience. We should abolish the paper selection committee forthwith and force speakers to engage in a battle to the death to obtain one of the available slots.
More seriously. There's a great deal of censorship involved in the entire process of running an event like this. Abstracts that aren't deemed "interesting" don't get picked. Speakers that have proven problematic in the past are likely to be frowned upon. Though I don't believe it's ever happened at LCA, it's plausible that speakers might be ejected from the conference for unrelated reasons before they have an opportunity to present. But you know what's wonderful about free speech? Anyone unable to present their opinions can choose to do so elsewhere, and anyone interested in those opinions can view them there. Crying "censorship" the moment someone is taken to task for breaching a policy that was voluntarily implemented by the conference organisers is ignoring the reality of the situation - to wit, speakers have never been at liberty to say whatever they want to, and likely never will be at this kind of event.