As far as current objections to final causes are concerned, I cannot point to any authors. I guess everybody simply thinks final causes are dead and buried. (To the contrary, I can point out a few current authors who argue that final causes are back with a revenge.)
When the times turned modern, objections to final causes have involved pointing out that there is too much supernatural or unempirical in them (as in statements like "this is how God made it" or "it serves nature perfectly"), too much subjective or vague in them (as in appeals to harmony or beauty) or that they do not seem like causes at all, but more like explanations with no necessary relation with causality (as in answers to most why-questions).
I personally think that the framework of four causes is an Aristotelian peculiarity that does not serve everybody equally well, and possibly arises from some translation problem http://www.borishennig.de/texte/2016/fourcausesbk.pdf
Boris Hennig wrote:
Aristotle says that in order to really understand a thing, we need to understand its aitia, and he distinguishes between four kinds of aitia. This term, aitia, is usually translated as “cause”. However, not all of Aristotle’s four aitiai are causes in the modern sense of this word. Perhaps none of them are.
