I think understanding this situation completely requires an enormous amount of empathy. Whether one agrees with the protesters or not, it's unfair to characterize them merely as fighting against freedom of speech. I am sure they recognize the speech aspect of this, but to them, that is second to what they perceive to be the central issue: equality. Arguable perhaps, but I hold that the issue of equality trumps that of speech.

This issue is related is part of a larger trend whereby arguably minor transgressions trigger significant protest (see the Atlantic's coverage of Oberlin). My take is that after an oppressed class completes the initial leaps and bounds toward equality, tactics of old (e.g. nonviolent peaceful protest) cease to effect further change. New tactics therefore must evolve in order to close the remaining gap. This gap is relatively small, but its size isn't the point - the fact that a gap, based merely on class identification, exists at all should not be accepted.

The current tactics might not be perfect - I posit they are still evolving. But they do effectively utilize available resources and processes (e.g. content virality) to draw massive attention to issues.

As for their characterization by MSM (e.g. the protesters are "bullies", they have fostered what is uncharitably called a "victimhood culture") we are simply observing (or participating in) the attempt to resolve cognitive dissonance between evidence of social inequality and the intellectual status quo.