Strangely enough, this is what Margaret Thatcher thought as well. She instituted a ban on the media directly reporting what IRA leaders said. What happened then was that you'd have video of one of their leaders - Gerry Adams, say - talking; and an actor would dub his words. Final score: UK Govt 0: IRA 1 (own goal by UK Govt).
The problem is that until you actually listen to someone with a grievance and deal with it you're just going to make that grievance much worse. This the British have (finally) done in Ireland - and not before time, either.
Another consequence of censorship - and that's what you're advocating, pushback - is that people on your own side start to wonder what you're trying to hide.
Far better to let them speak and let the people decide the rights and wrongs - as happened last week when Jimmy Young got a spokesman for Al-Muhajiroun, a British islamic fundamentalist group, to say that they "will continue to struggle and strive until we see the flag of Islam fly over 10 Downing Street".