We generally expect provider/customer relationships to be in good faith, and the generally expect free speech to happen in good faith, aka "I'm not relying on dirty tricks to persuade people." DS dropped their end, so I would feel no obligation to hold up my end.
I would oppose banning what they are saying in general, but I think it's entirely reasonable to no longer provide any services to them once they misuse the provider/customer relationship.
This isn't about content moderation to manage complaints. This is about protecting your company image specifically as a company that doesn't take sides.
DS tried to claim that the company was taking a side. CEO broke the relationship because of that.
If the CEO got complaints, and DS had said nothing about Cloudflare, and the company chose to drop the customer, then you'd have a point, but that's not what happened.