I've often said that the term/description "atheist" tell us so little. The author below provides some descriptions that are more meaningful.
Upon reviewing the list, I'm of the opinion that "religious atheists" are very common, but they are also likely to be "closet atheists".
17 Kinds of Atheism
‘Atheism’ is a much simpler concept than ‘Christianity’ or ‘Hinduism’, but the word atheism is still used in a wide variety of ways.
This can cause confusion. Someone may announce that she is an atheist, and her listeners may assume she is one type of atheist, when really she is a different type of atheist.
So to clear things up, here are 17 kinds of atheism, organized into 7 sets. Some kinds of atheism can be combined in a person, and some cannot. For example, it is perfectly consistent to be an agnostic, narrow, friendly atheist. But one cannot simultaneously be both a passive atheist and a militant atheist.
This list is not definitive. There are many ways to organize and label different kinds of atheism.
For brevity’s sake, I have substituted “gods” for the usual phrase “God or gods.”
1. Difference in Knowledge
A gnostic atheist not only believes there are no gods, he also claims to know there are no gods.
An agnostic atheist doesn’t believe in gods, but doesn’t claim to know there are no gods.
2. Difference in Affirmation
A negative atheist merely lacks a belief in gods. He is also called a weak atheist or an implicit atheist.
A positive atheist not only lacks a belief in gods, but also affirms that no gods exist. He is also called a strong atheist or an explicit atheist.
3. Difference in Scope
A broad atheist denies the existence of all gods: Zeus, Thor, Yahweh, Shiva, and so on.
A narrow atheist denies the existence of the traditional Western omni-God who is all-good, all-knowing, and all-powerful.
4. Difference in the Assessed Rationality of Theism
An unfriendly atheist believes no one is justified in believing that gods exist.
An indifferent atheist doesn’t have a belief on whether or not others are justified in believing that gods exist.
A friendly atheist believes that some theists are justified in believing that gods exist.
5. Difference in Openness
A closet atheist has not yet revealed his disbelief to most people.
An open atheist has revealed his disbelief to most people.
6. Difference in Action
A passive atheist doesn’t believe in god but doesn’t try to influence the world in favor of atheism.
An evangelical atheist tries to persuade others to give up theistic belief.
An active atheist labors on behalf of causes that specifically benefit atheists (but not necessarily just atheists). For example, he strives against discrimination toward atheists, or he strives in favor of separation of church and state.
A militant atheist uses violence to promote atheism or destroy religion. (Often, the term “militant atheist” is misapplied to non-violent evangelical atheists like Richard Dawkins. But to preserve the parallel with the “militant Christian” who bombs abortion clinics or the “militant Muslim” suicide bomber, I prefer the definition of “militant atheist” that assumes acts of violence.)
7. Difference in Religiosity
A religious atheist practices religion but does not believe in gods.
A non-religious atheist does not practice religion.
Of course, there are many more “kinds” of atheism than this, for one may be a Republican atheist or a Democratic atheist, a short atheist or a tall atheist, a Caucasian atheist or an Hispanic atheist, a foundationalist atheist or a coherentist atheist, an enchanted atheist or a disenchanted atheist.