II considere that a situation of uniformally acceptance of someone works is not so healthy.
I understand your point, but I still find this an odd statement to make in a forum devoted to classical music, the very concept of which presupposes a body of acknowledged "classics" that constitute the basic repertoire of acknowledged masterpieces and major works. This body of work is not completely monolithic. It evolved over time; works are added, and deleted as a function of what actually gets played. The case of Mahler is particularly interesting in that it illustrates the process of becoming a "classic" with singular vividness. So I would agree with you that complete uniformity is probably not healthy, but that is not what I see. What I see is a process of ongoing, gradual change, and to me that IS healthy.
As to conductors who do not play Mahler, Barry has given a very good overview, but more interesting (and fun) to me is the list of conductors who SHOULD NOT conduct Mahler. Barry finds Norrington entertaining just to hear something different. I too enjoy the occasional mustache painted on the Mona Lisa, but after one example the fun rapidly diminishes and becomes boringly predictable, particularly when the outrageousness is dressed up as serious historical scholarship. I also feel sorry for the orchestra, which is having a miserable time (I know for a fact) and knows just how terrible it sounds in Mahler and just about everything else.
It is very rare that any conductor avoids whole swaths of the standard repertoire--they have a professional obligation, particularly if they have a regular position with an orchestra, to put together varied and interesting programs that will attract an audience. Therefore it's a mistake to consider what they do in a vacuum. As an example, consider Mahler himself, whose programs with the New York Philharmonic included a lot of (then) contemporary music and pieces that he didn't particularly like, but which he knew the audience liked, or thought were important, or which worked well in an overall programming concept. We shouldn't assume that all music that a conductor plays, even very well, reflects a deep affinity with the composer or represents a larger aesthetic statement of some kind. Often he is just doing his job as any professional must.
So again, the fact that most conductors today will conduct Mahler I regard as a healthy sign of a modern professional at work. I wouldn't give it any deeper significance than that. As for those who refuse to conduct Mahler, some do it out of honest lack of sympathy for the idiom (like Wand or Celibidache), and others are simply using it to grandstand or create a specific persona (Thielemann, so it seems). And there is of course a third possibility that conductors will never mention, and which may be just as true--that they couldn't conduct the music effectively if they wanted to because they simply lack the technique, or don't believe that the players can master the music in the limited amount of rehearsal time available. This was certainly the case with Karajan and Berlin (remember 50 rehearsals for Mahler 5?), and it's a real issue both with conductors who don't conduct Mahler, and with even more who do.
When Hans Vonk took over St. Louis from Leonard Slatkin, I was astounded to read an interview in which he claimed he planned to do lots of Brahms (difficult given that he only wrote 13 orchestral works), but "of course" felt no affinity whatsoever for Dvorak. Now who doesn't like Dvorak? But evidently Vonk didn't. I respect that, and if audiences in St. Louis want Dvorak, then that's why God invented guest conductors. Still, it was very unusual, and it will become more so not because of the state of the arts in our society, but simply because orchestras are often full-time organizations asked to play week-in, week-out, and conductors have to conduct many more concerts than at any time in the past. So let us not lose sight of pragmatic considerations. Conductors who limit their engagements (as Giulini did in Los Angeles) enjoy the luxury of playing just the works that they feel closest to. Those who work more continuously need more music because there are so many more concerts, and Mahler has benefited from this trend as well.
Dave H