They then will proceed to find another place that is less easy to control to carry on with their message, and will have a renewed feeling of legitimacy and urgency.
What's even worse is that it may very well be used to censor even more things in the future, as people with a new toy tend to make use of it.
In the end, removing space to debate about hot topics like those will make the angry people feel like loosing even more respect (a big motivator in their initial believe), while preventing anybody else to build a sane approach to it (you need to be exposed to hate to be a functional member of an imperfect society).