It’s possible to be a Christian atheist, a Jewish atheist, a Buddhist atheist—in the sense of identifying with a religious tradition while disagreeing with its supernatural doctrines.
It’s especially possible to be a Jewish atheist. My wife is Jewish, and I’m a physicist, both which mean I get to hang around secular Jews a lot. More than half of the Jews of my acquaintance have no supernatural beliefs. Now, that is certainly not a representative sample, but nontheistic Jews are still common enough to become almost a stereotype.
Socially and doctrinally, Islam is pretty close to Judaism. The class of religious scholars (the de facto clergy) among Muslims, for example, are much like rabbis, rather than priests or ministers. But in the Islamic case, it’s very hard to speak of nontheistic Muslims. I know lots of secular Muslims, lots of nonobservant Muslims. But among those who lack interest in God or actively disbelieve in a God, a very small number to begin with, I have a hard time thinking of any who would also identify themselves as Muslim. Maybe one or two, and I haven’t actually asked. Nonbelief tends to push Muslims away from their identification with Muslim culture and tradition as well, perhaps.
I’m not sure if this is significant, but I think it’s mildly interesting anyway. At any rate, I’d be curious to know if my observation is accurate, or if it’s just my unrepresentative experience so far.