How frightened should people be about this? It would be odd not to be worried. The planet's history contains many less stable and clement eras than the Holocene. Who is to say that human action might not tip the planet into new instability?
Some will want simply to put the clock back. But returning to the way things were is neither realistic nor morally tenable. A planet that could soon be supporting as many as 10 billion human beings has to work differently from the one that held 1 billion people, mostly peasants, 200 years ago. The challenge of the Anthropocene is to use human ingenuity to set things up so that the planet can accomplish its 21st-century task.
Increasing the planet's resilience will probably involve a few dramatic changes and a lot of fiddling. An example of the former could be geoengineering. Today the copious carbon dioxide emitted to the atmosphere is left for nature to pick up, which it cannot do fast enough. Although the technologies are still nascent, the idea that humans might help remove carbon from the skies as well as put it there is a reasonable Anthropocene expectation; it wouldn't stop climate change any time soon, but it might shorten its lease, and reduce the changes in ocean chemistry that excess carbon brings about.
More often the answer will be fiddling—finding ways to apply human muscle with the grain of nature, rather than against it, and help it in its inbuilt tendency to recycle things. Human interference in the nitrogen cycle has made far more nitrogen available to plants and animals; it has done much less to help the planet deal with all that nitrogen when they have finished with it. Instead we suffer ever more coastal “dead zones” overrun by nitrogen-fed algal blooms. Quite small things, such as smarter farming and better sewage treatment, could help a lot.
For humans to be intimately involved in many interconnected processes at a planetary scale carries huge risks. But it is possible to add to the planet's resilience, often through simple and piecemeal actions, if they are well thought through. And one of the messages of the Anthropocene is that piecemeal actions can quickly add up to planetary change.