In spite of the fact that he has been dead for a decade, Stephen Jay Gould remains the authority on challenges to classical Darwinism and the hardened version of the Modern Synthesis (sometimes referred to as Neo-Darwinism).
If you really want to understand this issue then you have to read The Structure of Evolutionary Theory. One of my criticism of those who would overthrow modern evolutionary theory is that they are often completely ignorant of the work done by Gould and his allies and they end up attacking a strawman version of modern evolutionary theory.
Gould described the essential features of Darwinism in many of his writings. The most important feature is an emphasis on natural selection as the mechanism of evolution. In much of his work Gould emphasizes the roles of contingency, constraints, and non-gradualistic evolution as extensions of Darwinism. However, he doesn't forget direct challenges to Darwinism in the form of nonadaptive mechanisms that don't, under any circumstances, fit within the Darwinian framework.
These are complicated issues and that partially explains why so many people have not been able to follow Gould's reasoning. He doesn't help by using a writing style that requires your full attention. The advantage of that style is that he doesn't dumb down the subject and he covers all the exceptions and qualifications.
Here's Gould explaining why some features could arise as one form of adaptation then shift to serve another adaptive role (functional shift) (page 1246-1247). These features are called exaptations since they did not originally arise as adaptation to their present role. (Think of a defective transposon that becomes a regulatory sequence.)
Nevertheless, also emphasized throughout, ... the basic concept of exaptation remains consistent with orthodox Darwinism (while expanding its purview and adding some structural clarification and sophistication) for an obvious reason: the principle of quirky functional shift does not challenge the control of evolution by natural selection as an adaptational process. Unpredictable shift of function may establish the ground of contingency, and may imply a rule for structural constraints upon phyletic pathways. But this principle does not undermine the functionalist basics of evolutionary change because features so effected remain adaptive throughout: they originate from one function (presumably by natural selection), and then undergo quirky shift to a different utility.In other words, lots of things can't be explained by Darwinism even if they look adaptive today.
The deeper challenge posed to orthodox Darwinism by the principle of functional shift flows from the implication that, if current utility does not reveal the reasons for hisorical origin, then these initial reasons need not be adaptational or functional at all—for features with current adoptive status may have originated from nonadaptive reasons in an ancestral form. In other words, and in the terminology of table 11-1, when certain aptations rack rank as exaptations rather than adaptations, the coopted source will be identifiable as an ancestral structure with either adaptive origins (for a different function) or nonadaptive origins (for no function at all). ...
The general conclusion may be stated in a simple manner, but I believe that the resulting implications for evolutionary theory are both profound and curiously underappreciated: If many features that operate as adaptations under present regimes of natural selection were exapted from ancestral features with nonadaptive origins—and were not built as adaptations for their current use (or exapted from ancestral features with adaptive origins for different functions)—then we cannot explain all the pathways of evolutionary change under functionalist mechanics of the theory of natural selection. Instead, we must allow that many important (and currently adaptive) traits originated for nonadaptive reasons that cannot be attributed to the direct action of natural selection at all and, moreover, cannot be inferred from the exaptive utility of the trait in living species. Because the subject of evolutionary biology must engage many critical questions about the origins of features, and cannot be confined to the study of current utilities and selective regimes, nonadaptationist themes therefore assume an important role in a full account of life's history and the mechanisms of evolutionary change.