Person C operates a marketplace platform. They are very much involved in what is sold in their marketplace. They do not want to be associated with material deemed objectionable. They don't need you to agree it is objectionable. Do you think they should be forced to list anything someone might want to sell that isn't illegal? What kind of freedom is that?
If you don’t want to be associated with material that might be “objectionable” then don’t position yourself as a platform where arbitrary people can sign up and list whatever they want for sale.
Instead hire buyers to vet the merchandise you’re selling and stand behind it and take responsibility for it. You don’t get to have it both ways.
Where have they positioned themselves as such? They have always had control over what can be listed, they have never said you can sell "whatever you want". No marketplace has ever been what you are describing. Do you have any references that explain this ideology in more depth because I do not understand it.