So the authors are using 'field' to mean area of study which has standard usage in English I think so probably didn't need to be explained further.
When the authors wrote: "Nonetheless we think cataloguing these risks is important if we’re going to be serious about having an impact in important but ‘fragile’ fields like reducing extinction risk."
They are talking about 'reducing extinction risk' being a field of study. And the risks of doing damage to a that new field with early research.