To answer this charge there is no need to go to any trouble to claim that humanism isn't a religion. In the context of this particular controversy, it doesn't really matter if it is or it isn't. Also, no matter what we say about it, humanism is a religion to some people, even to the point of particular humanist groups like Ethical Culture. Different people see humanism differently: a religion, a lifestance, and a philosophy.
Furthermore, as the AHA uses the term "humanism," it does provide answers to religious questions. And so, by AHA’s own public principles, the AHA has an obligation to keep humanism out of the public schools. Is the AHA sincere about that? Yes.
The religious right defines humanism essentially as anything different from or contrary to their own views. It's thus a mere synonym for "sinner," "heathen," "worldly person," or person with modern ideas. That's why subjects as diverse as evolution, sex education, multiculturalism, globalism, comparative mythology, and so on get called "humanism."
What they all have in common is that fundamentalists don't like them. Never mind that Methodists and Catholics and most other mainstream religious folks have no problem with them. That doesn't seem to make them examples of "Methodism" or "Catholicism" in the public schools, at least as far as the religious right is concerned.
The AHA, on the other hand, defines "humanism in the public schools" as a theoretical, one-sided indoctrination of students in ideas unique and specific to humanist thought--such as the idea that we humans are alone in the universe; or that human values are derived solely from human nature, human needs, and human interest in the world of human experience. In other words, in order for something to be "humanism," it needs to be as clear-cut as any other teaching. Otherwise, it's just another state-of-the-art teaching in a subject, which only coincidentally comports with humanism.