Websites including the large companies like to portray themselves as non partisan platforms but in reality they are a corporations with distinct goals and objectives more like a newspaper. As such they will most likely follow popular opinion to maximize profit and readership (not unlike newspapers). They are not a public forum owned by the public like a university. I believe just like newspapers, websites, and churches due to free speak laws should be able to decide what is published and what is not. I think forcing websites to keep publishing "Authors" would have larger implications. I think a website or newspaper should always have the right to decided who is allowed to "publish" and who is not allowed to "publish". If a website is forced to "publish" an "author" I think this would be a greater damage to free speak. Any website (church, organization .. etc.) is then under risk of having to publish views that it disagrees with. True to free speech if anyone is "cancelled" as an "Author" they always have the right to open their own website to "publish" their content.
On the other hand we have to be very mindfully of what control large websites have and how they can control messaging similar to newspapers/radio/TV previously. You might say but large companies control which websites can be found. True but but if I look back in history before the internet there was more message control as then only the people with resources could start their own newspaper, flyer, radio to state their opinion. Now a website can be opened with very little money and there is many other search engines other the the normal ones. I would argue that it is much easier to get you view heard and seen than at any other time in history.
Let's use our opportunities wisely.
God help us to gain your wisdom
God help us to see through the fog
God help us to trust in you
God help us to be still and hear your voice