There are 8 billion people in the world. I'm not surprised some of them hold terrible ideas. The idea that some people hold X view so now we need to give the state Y power is insane with our population level because it can justify anything.

And who is to be the censor? Would you be so complacent if I were the censor, dictating what you can and cannot read, see, and hear?

The censor is the owner of the platform broadcasting the content. If I didn't like your censorship practices then I wouldn't use your platform.

Just to be clear, are you advocating for censorship on a platform (i.e. Facebook) level, or a governmental level as well?

I am not "advocating for censorship", I am "advocating" for the freedom to determine what content is hosted on a computer you own.

A computer owned by the government is a different story since government property is paid for by the tax-payer, so it should not be able to act unilaterally in matters of removing content.

And, out of curiosity, what would you say if someone made an argument that company X, while not owned by the government, is effectively a monopoly due in significant part to government intervention? Mechanisms for this might be: patent grants, regulations that create significant barriers to entry for new competitors, lucrative contracts with a federal department, inconsistent enforcement of existing laws while the incumbent has protective connections with the enforcers, tariffs...

Your hypothetical is too vague for me to answer. If you have a specific example I'd be happy to elucidate further.

I'll add that I don't regard patents, regulation, or "inconsistent enforcement of existing laws" as a reason why a company or individual should forfeit the freedom to determine what they host on a computer they own.

You have to keep refuting it for each new generation just like you have to teach each new generation the law of conservation of mass despite it having been proven over and over for centuries.

Then it is clear that the idea that the marketplace of ideas will simply defeat evil is a fraud. We will have to spend literally forever publicly arguing that it is a bad idea to murder everybody belonging to a given race.

We don't have a "marketplace of ideas" for alternatives for the conservation of mass. We teach kids one thing in school and move on. Why do we behave differently for other topics?

It is especially important for the more abhorrent ideas like "genocidal racism" to be exposed. Silencing it and driving it underground will have the opposite effect of what we want.

The reasons racism is wrong needs to be constantly reposted -- we forget and repeat our mistakes too often. That is why we have holocaust museums. In fact the dangers of racism become more obvious when you let the racists speak! Let them. Teach your children from them. Show them the effect.

Precisely how is an underground movement that cannot spread their ideas in public going to repeat the holocaust? How is forcing people to stay silent about their nightmarish beliefs going to possibly be worse than what we've already witnessed?

People just take it as an axiom that forcing ideas underground makes things worse but that seems like an idea that requires some support.

Racism is a security vulnerability in our brains. These ideas aren't propagated through reason. They are propagated by exploiting cognitive loopholes. Sitting down with your kid and showing them a whole bunch of fascist propaganda and then having a rational discussion with them isn't going to have the effect you want.

I'll quote Steven Pinker

    "Sunlight is the best disinfectant," according to Justice Louis Brandeis's 
     famous case for freedom of thought and expression. If an idea really is false, 
     only by examining it openly can we determine that it is false. At that point we 
     will be in a better position to convince others that it is false than if we had 
     let it fester in private, since our very avoidance of the issue serves as a 
     tacit acknowledgment that it may be true.

     https://www.edge.org/3rd_culture/dangerous07/dangerous07_index.html

This is not evidence, it is merely stating it as truth.

What of ideas that we have already determined to be false? Genocidal racism is garbage. It has been known to be garbage for a long time. Yet it persists. Must we continue having public discussions about the merits of genocidal racism? Can we stop in 10 years? 100 years? 1000 years?