Taken in the context of the chapter of Brave New World and the paragraph that it is in, this sentence is very significant. For, it points to the character flaws of Bernard Marx. While he understands that there are aspects of his society that are deserving of criticism, he wishes for the adulation of people and the attention that his bringing of John to the New World has brought him. In short, Bernard is a hypocrite:
Success went fizzily to Bernard's head and in the process reconciled him (as any good intoxicant should) to a world which, up till then, he had found very unstisfactory. In so far as it recognized him as important, the order of things was good. But, reconciled by his success, he yet refused to forego the privilege of criticizing this order. For the act of criticizing heightened his sense of importance, made him feel larger. Moreover, he did genuinely believe that there were things to criticize. (At the same time, he genuinely liked being a success and having all the girls he wanted.)
Clearly, Huxley is satirizing the man who fancies himself a "free-thinker" when he actually is subservient to a system; he only pretends at criticizing, performing it so he can "feel larger." In addition, Bernard's character also supports the flaws to the utopian system since he does not follow the design of his character. In contrast to him, Helmholtz Watson is truly an independent thinker.
What this sentence is saying is that Bernard Marx is trying to have it both ways. He has been reconciled to the society -- in other words, he has come to like the society when he used to dislike it -- because he has gotten to be a celebrity. But yet he still likes to criticize the way the society runs. That's what the second part of the sentence means -- he will not stop criticizing the "order" of the society.
Bernard wants to be seen as a rebel, but he also likes all the benefits that come with being a big shot in the society.