Are religious people cognitively different from those who are atheists?

Of course they are.* Just as people who like thyme are cognitively different from those who do not like thyme. What else would cause them to profess diverging beliefs?

Now, are there differences in the general architecture of their minds? That comes down to definitional issues: Would you say 'No general difference, they have all the corresponding brain areas'. Or do you zoom in to the level on which individual beliefs necessarily manifest themselves in conglomerates of grandmother-type neurons and assorted structures, then call that a general difference?

Would you count the correlation between anthropomorphizing your environment and not having a lot of knowledge of said environment, a la caveman versus grad student? In that case if you were able to differentiate educational sophistication based on e.g. future brain imagining methods, you could by proxy predict religious beliefs. Good enough to answer the original question in the affirmative? It would also predict ability to drive a car.

Supposing there were a difference in the general architecture on a level that most people would call "general architecture" (?), we could then try to ascertain the relative importance of hereditary ("nature") versus post-natal (or even in utero) environmental ("nurture") factors.

Going down that avenue, we'd note that the genetic drift and other genetic evolutionary factors for the last couple of centuries have been negligible (make that since the cro-magnons, if you're feeling charitable). Yet the proportion of religious believers has varied enourmously over short spans of time, even in homogeneous / steady gene pools (or subgroups, disregarding migration) such as Western Europe.

That leaves the question whether those environmental factors that do lead to different religious affiliations - by necessity changing your cognitive characteristics - effect a large enough change for that change to be classified as a "general architectural" change or not.

Apologizing for the verbosity, my point is that different valid studies may well show rigorous but contradictory results for that precise question, rooted in the exact formulation of what constitutes different general architectures. Unless someone is a dualist, all beliefs must leave their marks somewhere in your wetware, changing it. One of my biggest peeves in the field is just that - prima facie interesting niche results that are mutually incompatible because of minor variations in the problem definitions.

(* For sufficiently large concepts of "different")

Are religious people and atheists together different from people who don't care about religion?

None of them.

'In 2006 Steven Pinker wrote an unfavorable review [12] of Lakoff's book Whose Freedom? The Battle over America's Most Important Idea. Pinker's review was published in The New Republic. Pinker argued that Lakoff's propositions are unsupported and his prescriptions are a recipe for electoral failure. He wrote that Lakoff was condescending and deplored Lakoff's “shameless caricaturing of beliefs” and his “faith in the power of euphemism”. Pinker portrayed Lakoff's arguments as “cognitive relativism, in which mathematics, science, and philosophy are beauty contests between rival frames rather than attempts to characterize the nature of reality”. Lakoff wrote a rebuttal to the review [13] stating that his position on many matters is the exact reverse of what Pinker attributes to him. Lakoff explicitly rejected, for example, the cognitive relativism and faith in euphemism described above, arguing in favor of a deeper understanding of rationality that discards the modal logic conceptualization of rationality in favor of the better supported framing conceptualization'