So? Does ebay have a responsibility to host every listing that is submitted? Of course not.

According to what? A social contract? The written law? Some ethical/moral foundation?

The answer depends on what standard you're using.

In my opinion, yes they do have that responsibility. Once you attain a level of social and economic power on par with eBay, you have the responsibility to ensure that your actions do not limit free access to information.

If we were talking about a company that does 10k in sales a year -- they do not have that responsibility. But since we're talking about a company that does 4B in sales a year -- yes, according to my moral foundation, they do have that responsibility.

I value free speech and the freedom of expression pretty high on my list of important things though, while it seems like you value the ability of a billion dollar corporation to profit and maintain their brand image much higher than that.

Like I said, different moral foundations.

Probably good to start with 'legal responsibility' and then make the case that the law is morally wrong.

But in USA, they don't really have to list anything they don't like.

I don't think discussing the current state of US law is particularly interesting. My argument is from a moral standpoint.