how can we protect people without this censorship?

We don't, nor should we try to.
Protecting people's feelings from offense is not a valid activity in a free society. The second you start down the road of 'we must regulate this guy's words and actions to protect that guy's feelings' we become a nanny state full of people with paper thin skins. We accept that one consequence of free speech is that sometimes people will say things that are hurtful. We do that because the alternative is getting rid of free speech.

Hate must be addressed at its root.

I could not agree more. Fighting hatred with hatred only breeds more hatred. But that seems to be the standard strategy today, it's okay to not just refuse to tolerate intolerance, but to be actively intolerant of those who themselves seem intolerant. It is just fighting bad with bad and the result is more bad.

The way we fight the roots of hatred is with open discourse. The people who have hate in their hearts, we do not isolate them, we do not wall them off from society, we do not practice and encourage intolerance against them. We show them a better way. We make ourselves examples of doing better, not just against the people they don't like, but against the people we don't like.

We try to build bridges and encourage communication. For all the people who say immigrants are lazy lawbreakers, we show them immigrants who are the hardest working motherfuckers there are and pay their taxes. For the people who think black people are a problem, we introduce them to black people who break their stereotypes.

For the overwhelming majority of people who have hate in their hearts and intolerance and prejudice, those feelings are based on stereotypes.
People don't join the KKK because they start in a mixed culture and then conclude black people are a problem. They join the KKK because they have stereotypes they see reinforced in media and TV.

There was a famous Black dude whose name I don't remember, but he of his own volition managed to deprogram a whole bunch of KKK members. All he did was sit down and fucking talk to them. That's it. Like sit down at the bar next to them and start a conversation. Many of the KKK members had never encountered a respectable well-spoken black person before (let alone one willing to talk to them) and were completely blown away because it broke the stereotype of a black person that they joined the KKK to fight against.
A good number of them ended up leaving the KKK and giving this man their robes on the way out. So there's this friendly black dude who has a big box of KKK robes that were given to him by ex-members he deprogrammed.

That is how we fight hate. We fight hate with love, we fight intolerance with tolerance and open arms, we fight stereotypes with exposition, we fight ignorance with knowledge.

Otherwise it's like we are saying there's too much stupidity in society so we're going to prevent people with lower IQs from attempting school. It doesn't work.