I don't think anonymity is the central thing that changed the world, or the primary value of the internet. Anonymous voices are easy to falsify, so it's impossible to distinguish whether the comment represents a belief held in good faith, commercial spam, a prank, etc., and this limits the influence of online anonymity.
My belief is that the internet actually allows people to further insulate and isolate from minority POVs. Even though someone can butt into many online conversations without an invitation, this technique is interpreted as disruption and will typically only harden someone against the other side's influence.
Worse, the interfering party's humanity and commonalities are invisible to the other side; the disruptor is embodied merely as a wall of text to be torn apart, an inanimate object, instead of an earnest, sympathetic fellow being operating in good faith to contribute his/her POV to the discussion.
In the real world, the necessity of ongoing interaction with the same set of people requires everyone to at least tolerate the diversity of POVs with a bit of respect and decorum. Over time, as people grow closer and new data becomes visible, that perspective may become less and less foreign, and the good aspects of its owner revealed through regular interaction will more commonly prevent wholesale dismissal of people with a contrary POV, because there will be direct personal experience with a Real Person who holds it.
On the internet, no matter how crazy or isolated your beliefs/ideas are, you can find a cloister that will (at least appear to) parrot them back. Many people will isolate further and further into this group and feed off of each other with no input from the other side, allowing their caricatures to become more and more egregious and detached, leading to ever-increasing hostility and ultimately full dehumanization of those holding opposing POVs.
Of course, that isolation effect is not exclusive to the internet (cf. any wartime propaganda about the enemy "other", with whom most citizens would've had very little exposure), but IMO the internet allows it to occur more aggressively than ever. Anyone can retreat into their echo chamber after they've grown sick of the basic cohesion necessary to function in meatspace.