No, C is wrong because it is irrelevant to the reasoning that leads to the conclusion since it reverses the necessary/sufficient relationship of shame and feeling responsible. The stimulus says,
Acceptance of scientific theories that regard humans as subject to natural forces -> General moral decline
Not feeling responsible -> Unashamed about acting immorally -> People act immorally -> General moral decline.
C is wrong because it addresses what people who feel ASHAMED do. Why do we care about them? If it helps, diagram it:
Unashamed -> Immoral
~ Immoral -> ~Unashamed
In English, the second of these translates to:
Moral -> Ashamed
So from the stimulus, we know what Unashamed people do (act immorally), and we know what Moral people do (are ashamed when they act immorally,) but we don't have any idea what Ashamed people do. Being Ashamed is a necessary, but not a sufficient, condition for acting morally.
The thread of logic in the conclusion is sound, EXCEPT that we don't know where that first bit came from. What do scientific theories have to do with anything? Well, that's where answer choice B comes in. It connects Scientific theories to Not feeling responsible, therefore eventually connecting it to General moral decline.
Hope that helped!
In addition to this, what helps me with assumption questions after I've narrowed it down to two answer choices is negating both answer choices and seeing which one attacks the argument presented in the stimulus. Whichever one attacks the argument is the correct answer. In this case, if it was the case that "human beings who regard themselves only as natural objects will not
as a result lose their sense of responsibility for their actions" then that would directly contradict the conclusion of the argument and is therefore the assumption the argument makes. Hope this helps.