The question is too simplistic. A better question would be... To what degree are human beings part of nature?
What does appear to be true, is that human beings are more and more being disconnecting from nature, ever since they first made fire and every other invented discovery, that combines different chemical elements since that 'warming' discovery.
Every technological progression can be said to be a step up the ladder of man-made discoveries and those discoveries do begin to sever our connection to nature. There is no doubt that mankind is beginning to wrap itself in a technological bubble, that separates us from the more hostile elements of nature.
On the other hand, to ask the question 'are human beings still part of nature?' - Is an assumed question that doesn't beg the right answer; because it is most obviously the wrong question...
Indeed, no biologist would make the claim that mankind is not still part of nature. If we look at viruses that attack our bodies and survive within bodies because of the evolutionary process of natural selection, then to that degree at least we are still a part of nature.
To say that mankind is no longer a part of nature on one hand and to then say that mankind is still prone to attacks from viruses is an oxymoron. If mankind was not a part of nature as an absolute, then virus infection would not be possible. A biological virus by definition, can only parasitically live of biological hosts.
Now, a different question to ask would be: Are human beings still evolving through the process of natural selection? - On the surface this may sound like the same question as: 'are human beings still part of nature?'. But it is not the same question.
To the degree that our biological processes rely on nature, such as our need to inhale oxygen and expel carbon dioxide for example, then by that degree and other degrees of the same 'nature' we are part of nature.
But whether we are still evolving in the Darwinian sense, is a tougher question to answer. The evolutionary process does rely on natural selection. But the "survival of the fittest" has less significance in a technological society, because those pressures are weakened through technological advances that counter those pressures. Indeed, we may be at a stage of technological progress that means evolution by natural selection will have little or no effect over say, the next 10,000 years. Because as technology advances, natural evolutionary pressures on mankind are minimized, through technological progress.
The fact that we are still part of nature, does not mean that we always will be. Our technological revolutionary progress is very rapidly outstripping natures slow evolutionary processes and we are more and more encasing ourselves in a technological bubble beyond nature.
As one example of mankind's technological leap, we are already beginning to replace warn-out nature evolved body-parts, with technologically designed body-parts. Indeed, scientists are already talking about making artificial body-parts made from 'metal nanobumps' and nanobumps could also potentially be used to repair clogged blood vessels.
In fact, we now rely on technology far more than we do nature. Indeed, think of just one day in your life and how your very survival relies on man-made technology. How would mankind cope if all our technology suddenly disappeared overnight? - A frightening thought. Many of us would probably die and those that did survive would probably revert to some form tribalism or even barbarism.
As one example of how much we now rely on technology is the World Wide Web. 20 years ago it did not exist. But now it has become an intrinsic part of mankind's daily life and many business's today are entirely Internet driven. It is a completely different technological paradigm and has also become an indispensable one. If the World Wide Web collapsed tomorrow, it would devastate economies Worldwide and much of society would come to a grinding halt.
So, the answer is that yes, to a degree human beings are still a part of nature. But the degree by which we are is shrinking to a smaller and smaller point and may well one day collapse into a technological singularity and at that point we will have totally disconnected from nature.