I don't agree with your blanket statement that new atheists dismiss the idea of an independent world. I don't doubt that some people (atheist or not) hold that

I don't agree with your blanket statement that new atheists dismiss the idea of an independent world. I don't doubt that some people (atheist or not) hold that view, but I don't connect it at all with atheism. One counter to the claim that consciousness constructs the world, we could have some event witnessed by two independent observers. If the observers agree on what they witnessed, what explanation would there be that they just happened to construct the same event? Personally, I feel the physical world exists independent of conscious observation. On the other hand, what we think we are observing clearly is affected by our flawed perceptions and our flawed consciousness.