If you suppress a group like this, you don't make it weaker - you make the members more angry and more extreme in their views as they will feel persecuted and become even more convinced that their way is better. You push these people to become both more extreme and more hidden - a dangerous combination.
Where extremism is concerned, I think this claim is wrong far more often than it is right. As we've seen with social media, extremism is more like a very addictive drug. Many may have a predilection towards extremism but simply not be exposed to it in regular society and live productive, happy lives.
We like to think people who engage in acts with serious consequences are truly dedicated to their task. What we find (and I'll admit I find quite frightening) is how fickle certain people are about such cataclysmic decisions. Read interviews with various Muslim terrorists: "Well, I was either going to blow up America, or become an Air Conditioning repair man, and I was sick on exam day for A/C school." (not literally). The vast majority of minds that tend toward extremism are capable of doing great damage, but aren't particularly strong.
Certainly we see this with suicide. You would figure there can be no greater, more significant decision than to take one's own life. Yet the simple expedient of making it difficult to commit suicide from a recognized landmark has saved thousands of lives because those suffering just aren't that determined to carry it out if their preferred method is thwarted.
Now, this of course brings us to what should be censored, and I don't think this is either easy or safe to determine. But the idea that censorship doesn't work is more a much desired fantasy than fact.
Also, like a virus, extremism needs both a receptive host and an effective means of spread - communication. Traditionally in American society, there hasn't been a large receptive body. But I think in the last 20-30 years, the US has grown subpopulations that *are* receptive hosts, most likely due to the declining status of poor, less-educated whites with respect to various visible minorities. (Essentially a repeat of post-civil war turmoil when some of the southern population turned to extremism like the KKK to defend their status against freed blacks. No matter how far down the totem pole of status you were, there were always visible minorities below you.)
I think in another 20-30 years, when we reach a new equilibrium, I don't think the call to extremism will be quite so strong, but right now, we have a lethal cocktail - a lot of people primed to embrace extremism, and vastly easier communication mechanisms that can expose people to such extremism, be it flat-earth, or white nationalism.