What renders atheism incompatible with a coherent account of morality, when it is incompatible, is physicalism (or what is sometimes described as reductive materialism). If it is true that the universe consists entirely and without remainder of particles and energy, then all human action must be within the domain of caused events, free will does not exist, and moral reasoning is futile if not illusory (as are other kinds of reasoning).
This is a stupefyingly widespread view that flows from an elementary error in thinking.
Suppose you know that there is free will or that moral reasoning is not futile. Next, suppose you find that the universe is made out of only whatever the universe is made out of. What do you infer? You infer that free will and moral reasoning, which occur inside the universe (or as aspects of the universe), whatever they may be, are made possible because of whatever it is the universe is made out of. And there you are.
Here is what you do not do. You do not start with a mystifying conditional like “If the universe is only physical (or whatever), then there is no free will,” because how do you know that? You don't. But you may think you do and so you get caught in a retarded ponens/tollens showdown: the universe is physical, ergo no free will, or… free will, so the universe is not physical. But, again, through what method of divination do we validate this conditional? None. Because we already know it is false.
Here are two things you know: free will exists (it is obvious: go ahead, touch your nose) and the universe is made of whatever it is made of (obvious, if anything is). Therefore, you know the conjunction of those two things. Therefore, you know that the crazy proposition that says that one of them must be false isn't true! There's no need to get hung up on an arbitrary conjecture about the trascendental conditions for the very possibility of the existence of something when things you already know rule it out. P & Q implies ~ (P —> ~Q). Logic: try it!
If we find out tomorrow that the universe is made of jello, all we will have learned about morality is that it, like everything else, is ultimately jello-dependent.
Will Wilkinson 