What does "working mathematician" mean? What does "working mathematician" mean? Is this term derogatory? What properties of a "working mathematician" are considered undesirable, and what attitude contrasts them?
 A: The term "working mathematician" has been occasionally used to distinguish mathematicians from metamathematicians (those working in foundations, logic, philosophy, etc). This term predates Mac Lane's book on category theory. For example, it was used by Bourbaki in his 1948 ASL address Foundations of Mathematics for the Working Mathematician as well as in his Elements series. Below are some pertinent excerpts from Chapter 7 of Leo Corry's book.

It is not unusual to come across pronouncements of Bourbaki members,
  who insistently characterize Bourbaki’s approach as that of the “working
  mathematician” whose professional interest focuses variously on problem
  solving, research and exposition of theorems and theories, and which has no
  direct interest in philosophical or foundational issues. Thus Bourbaki formulated
  no explicit philosophy of mathematics and in retrospect individual members
  of the group even denied any interest whatsoever in philosophy or even
  in foundational research of any kind. (Jean Dieudonné (1982, 619) once summarized Bourbaki’s avowed position regarding these
  kinds of questions “as total indifference. What Bourbaki considers important is communication between mathematicians. Personal philosophical conceptions are irrelevant for him.”)



Thus, in spite of declarations to the contrary elsewhere, Bourbaki
  here implicitly admitted (concealing this confession, as it were, in a footnote)
  that the link between the formal apparatus introduced in Theory of Sets and the
  activities of the “working mathematician” (Bourbaki’s declared main
  addressee) is tenuous, and, at best, of purely heuristic value.

See also these excerpts from Kneeebone's Mathematical Logic and the Foundations of Mathematics, an introductory survey.

Hilbert's outlook
  was accordingly that of a working mathematician, and the opinions
  that he expressed at the Paris congress may thus be taken as direct
  testimony from a mathematician as to the nature of his activity. A
  comparison at once suggests itself with certain utterances of Nicolas
  Bourbaki, who has a clear right to speak for the mathematicians of a
  more recent generation, and we find indeed that Bourbaki confirms
  much of what Hilbert has said or implied. Bourbaki has remained
  very much a working mathematician, and he has not made any 
  systematic study of the foundations of mathematics such as that which
  Hilbert undertook in his later work.



Russell's Principia Mathematica and Hilbert's
  metamathematical investigations, and equally the various intuitionist
  and constructivist undertakings that we have been examining, were
  concerned less with helping the working mathematician to attain the
  rigour that he seeks in the actual presentation of mathematical theories
  than with answering fundamental questions that arise in the realm of
  philosophy of mathematics. In recent years, however, mathematical
  and metamathematical inquiries have been found to converge, and now
  at last the working mathematician and the metamathematician or
  logician are able to re-establish contact.

A: To me, it means a mathematician that is active, i.e. publishing research. 
A: I was trained as a mathematician but work in industry on algorithms, usually of a probabilistic inference or machine learning flavor.  I rarely publish, but for what it's worth, I still think of myself as a "working mathematician".
A: The way I understand it the working mathematician is a mathematician which works, researches, publishes.
I recall seeing this mainly in the context of "Theory X for the working mathematician" which means a mathematician which is not particularly interested in X, but knowing about it could help, and would help. For example surely most mathematicians won't care about large cardinals, but if there was a method based on large cardinals which would have solved a lot of problems it would sure be nice if one knows about it even if they are not set theoretically inclined. In such case a book called "Large cardinals for the working mathematician" would be a reasonable titled book.
If I were ever called a working mathematician I'd be insulted, but then again I believe that lack of work is much harder than work. Mathematics just writes its own! :-)
