Having given an answer that responds to the surface of the question, I would like to give a different one that I feel addresses its core.
Atheism does not need to meet this criticism at all. It should not accept the golden rule, or some moderate refinement of it, as a basis for ethics.
This principle is simply a warmed-over compromise between religions, abstracted out of what they tend to have in common. We like it because most modern atheists are from traditions where it is prominent, and because the idea is simple.
But atheism is, by its nature as a 'negative principle', pluralistic at its basis. There are many, many reasons to have a religion, and the motivations not to include multiple objections to each of those. There is not a single core of atheism, and atheists of different stripes, in general, should find ethical systems that represent their true motivations.
For instance, an atheism motivated like Dawkins', flowing from his understanding of our species' biology, suggests we learn from evolution and choose a tenable principle in accord with our nature as animals. This has a framing largely in line with Nietzsche's call to be 'beyond' good and evil and to make the 'art of the self' the primary ethical motivation.
Art does not need an audience, but it is always better when it expects and finds one. To make art of the self, then, involves other people, and so you cannot alienate or destroy them. You have a good use for their regard and their ideas, and for that reason, you need their respect.
The alternate form of this is 'follow the will to power', but it is too easily misunderstood. It is easy to see the power of destruction, but, in general, it is a short-sighted option that betrays a lack not just of wisdom, but of taste, including awareness of your environment and how you use it.
So, working dialectically, I might refine the Golden Rule by opposing it: "Do unto others as you, as an animal, naturally do. When that precipitates undesirable responses, adapt. But adapt as a social primate with a wide vision of the world: in a way that protects your cultural standing, contributes to maintaining your social structures and does not forestall the future development of your individual relationships."
The enneagram came up in response to the first answer, in those terms, that answer conveys position '2' -- serve others. Kant's position is ultimately '9' -- make peace. The most common contrast to Kantian ethics, Mills' utilitarianism is from position '5' -- analyze and optimize. Nietzsche's is closest to '8' -- fight smart.
(And despite its whole "Madam Blavatsky" Ouspensky/Gurdieev history, the structure is not as esoteric or niche as it seems. It is the same structure that a dominant school of psychoanalysts use to diagnose personality structure -- see McWilliams' "Psychoanalytic Diagnosis", which includes these same nine stable positions in the same order, but starting from a different point in the sequence, and therefore presenting the same intermediate options. She adds a tenth arguably 'unstable' position in the 'dissociative' core. There are easy mappings from psychoanalysis in general onto other personality theories.)
Given a structure like this, one might expect five (or six if McWilliams is right) more answers that agree better with different motivations to choose a moral path outside dogma.