It's hard to know where to put Scientology. Again, is it a cult, or a religion, or a psychosocial pyramid scheme based on absolutely terrible science? Decisions, decisions.
The one thing that is ``clear'' - the state towards which Scientology is suppose to move one once one has paid enough money to its auditors - is that Scientology doesn't say much of anything about God. Oh, there is a ``Supreme Being'' alluded to here and there, maybe, but Scientology isn't about worship and doesn't assign any particular attributes (that I know of, at least, as an admitted outsider) to that Being.
So it's hard to say if this Being is consistent with the theorem above, not that it really matters. Sure, why not? Or, maybe not. Other than that, the teachings public and private of this ``religion'' resemble a mixture of really, really bad Science Fiction (the only kind L. Ron Hubbard wrote, although as a long running SF fan I am fond of one or two of his space opera stories, e.g. ``Battlefield Earth'') and quack psychiatry. It makes various supernatural claims (such as the existence of a ``soul'' that survives death, called a thetan, a process of transcendent judgement that determines the progress of that soul along the path to clarity based on the quality of its embodied life - in a lot of ways, it is like Buddhism (another not-really-a-religion), and hence it quite naturally attracts people in much the same way.
However, to be a Buddhist all one has to do is say ``I am a Buddhist'', accept the Four Noble Truths and begin to practice the Eightfold Way and poof! You're a Buddhist! Nothing to sign, no need for a church, or priests, or donations. If you feel really inspired and want some organization, you can go whole hog and become a Buddhist monk and retire from the world, but Buddhism is essentially egalitarian and purely lay practice is perfectly all right and even was specified by the Buddha long ago (and, given a lack of evidence from reincarnation, is probably a more ethical form of Buddhism because if one has only one life to live it is hardly ethical to ask other people to work to support you with alms when you are perfectly capable of supporting yourself).
Not so Scientology. I cannot just sit here and say ``Gee, I think I'll be a Scientologist''. It costs money to be a Scientologist. Nor can I just go to the Internet or a bookstore to buy a book to learn the practice of Scientology (they way I can Buddhism or Hinduism or Christianity or Islam) - it is chock full of ``secret teachings'' that get increasingly wild and unbelievable as one ascends its highly selective inner circle. It costs money to be audited, and one has to be audited many times to reach the inner circle.
So, church, cult, pyramid scheme? You decide. All that is absolutely certain is that it is almost as dangerous to tweak the tail of Scientology in any public forum as it is to wear tee-shirts with pictures of Muhammed holding up a poster saying ``Support freedom of political and religious thought! Wear my picture on your tee-shirt!'' - except that where Islam issues fatwahs calling for your death or administers ad hoc beatings on public streets for this sort of blasphemy, Scientology responds with lawyers and lawsuits funded (one must assume) from its vast coffers of money extracted from all of those people being audited! What was that part about the first amendment, again? Did I miss something?
Let me be clear about one thing. I personally think Scientology is a complete fraud, a pyramidal cult, not a religion at all. That makes me at the very least a suppressive personality if not an active hopelessly antisocial personality, which is also de facto proof that the church's psychology is complete bullshit, as I actually get along fine with children and pets, am generally liked by my colleagues and students, and am happy and well adjusted in life. I'm already ``clear'' in that I know exactly what I know and why I know it right down to the axiomatic basis of the knowledge and why it is arguably the best set of things for me to believe. Can any of them say the same? The day they put salt on the tail of a thetan and publish the results in Physical Review, maybe...
That does it for major theisms, although as I said one or two of the religions above aren't particularly major and one or two aren't really theisms.
Note Well! My critique above, regardless of its polemic nature, is a perfectly reasonable analysis based on the theorem I prove, accepted scientific knowledge, and the best secular morality I can muster on the basis of reason. This does not mean that all Scientologists, Jehovah's Witnesses, Mormons, Muslims, Christians, Jews, Buddhists, or Hindus are bad people. They are mistaken people to the extent that they believe in an impossible God that is omniscient but distinct from the Universe. In many cases, their theistic scriptures can easily be shown to contain bad things - lies, myths, legends, the immoral presented as the moral - suggesting that at the very least those scriptures need to be rewritten, purged of all of the obvious nonsense, keeping the good parts, and adopting a Universal view of God that will inevitably bring the theisms into convergence.
After all, if God exists, there is only one set of religious assertions that is correct. Prophecy and divine revelation have proven a most unreliable way of obtaining the truth about God - a statement that doesn't even require proof beyond the observation that the world is splintered between hundreds, thousands, tens of thousands of religious cults and schools and churches, with complete disconnections in their theistic support and with substantial contradictions between all of them. In science, when two people make competing claims, there is a systematic way of deciding between the two based on evidence and on how well the explanations fit into the entire body of reason, and inevitably scientists make the best decision when and as the evidence and arguments warrant it, reserving the right to change their minds later on the basis of new evidence or arguments as needed!
Why doesn't this happen in religion? Because religion relies on authority, divine revelation, and an income stream obtained from the faithful that makes apostasy or alteration of creed bad for business. Because religion turns away from reason and asks people to believe in spite of the fact that their beliefs are hopelessly contradicted by common sense and science. God couldn't possibly have constructed a lying Universe, but the only way that e.g. Genesis could be correct is if It did! If religions made a real effort, they could pull a decent morality out of the union of their scriptures, augmented with secular conclusions as needed. They could adopt an ecumenical Universal God. They could encourage their adherents to use reason and not faith when deciding what to believe. And the conflicts associated with religious differences would silently vanish from the world scene - peace in the Middle East being the least of the consequences.
So no, all of these faiths or philosophies have good aspects and bad aspects and have adherents who are lovely, non-violent people who try their very best to live moral lives by any standards. Viewed as metaphor, as mythopoeic literature, some of their stories are very worthwhile and can teach valuable lessons. This has nothing to do with whether or not their basic supernatural or moral tenets are correct. If the model of God they hypothesize is not in agreement with a God who is the Universe, then that God is impossible - it cannot be omniscient. With this we conclude our summary of the principle theisms.