The good pastor Henderson neglects to mention that, following his approach, there can be no such thing as a good theist either. All morality is ultimately subjective, even if and when some intellectually incompetent dolt reasons that his or her morality is made objective by his or her belief in a supernatural entity that sanctions it.
For, in the first place, there is no means whereby a theist can escape the fact they are basically guessing when they assert (1) there exists a supernatural entity and (2) that supernatural entity sanctions a certain morality.
Second, even if 1 and 2 above could be demonstrated to be true, that would not in itself lead to the conclusion that morality was objective because it could still remain the case that the supernatural entity sanctions not only the morality in question, but several or even all human moralities at once.
Last, even if 1 and 2 above could be demonstrated to be true, and it were also true that the supernatural entity sanctioned one and only one morality, it would still not be the case that that morality was an objective morality in any meaningful sense of the word "objective". After all, what does it mean to have an objective morality?
Surely, an objective morality would in theory be the same as an objective fact about the natural world. But facts about the natural world do not necessarily exist ontologically. Instead, they are ultimately subjective facts that are inter-subjectively verifiable, which might give them the appearance of existing ontologically.
So is there objective morality in the sense of an inter-subjectively verifiable morality? Apparently not, given the diversity of opinions regarding what is moral and immoral. Or, if there is a consensus, the consensus might be due to other factors rather than to the allegedly ontological existence of morality. Hence, the notion there is an objective morality in the same sense that there are objective facts seems very likely to be vapid and devoid of genuine meaning.
But I suspect that Henderson would fail to understand any of that even though -- so far as I can see -- it is little more than a logical extension of his own basic approach.