I would say that there are two main trains of thought which push me towards Moore's way of thinking about organized religion. (And I'm not saying that I agree with him, just that I'm not unsympathetic.)
One "train" comes from thinking about the essential centrality of "La ilaha illa Allah" (no god but God) in Islam. Both too good to be true? and no god but God give orthodox references which strongly suggest that the only condition for salvation is sincere belief in "no god but God". That's it. The answer. The only requirement. Nothing else. And everything else is extra. I'm not trying to give a fatwa here. I'm just saying describing what comes to mind when I read those particular hadith.
But if tawhid is the only requirement, then what are the rest of the Islamic laws and principles for? Well, many of the religious practices (ibadat) like reading the Quran, salat, dhikr) are primarily means to reinforce and sustain a belief in La ilaha illa Allah. After all, mankind was made forgetful. Another portion of shariah's guidance provides sound advice for living a good individual life. And of course, much of the shariah is related to promoting a peaceful and justly ordered society (which some may think of as social control). In any case, I would say that the more an individual is impressed by "no god but God", then these other functions of Islamic law would tend to fade in significance along with every other trapping of organized religion. As the hadith goes:
Volume 1, Book 3, Number 131:
I was informed that the Prophet had said to Mu'adh, "Whosoever will meet Allah without associating anything in worship with Him will go to Paradise." Mu'adh asked the Prophet, "Should I not inform the people of this good news?" The Prophet replied, "No, I am afraid, lest they should depend upon it (absolutely)."
A second train of thought which makes me sympathize somewhat with Moore's critical attitude towards organized religion starts with thinking about the legacy of Malcolm X. Malcolm is often presented as a "poster boy" for Sunni Islam, but if you stop to check, he actually spent much more time as a member of the Nation of Islam than he ever spent as a Muslim outside of the Nation. (He was assinated less than a year after he left the Nation). Secondly, I don't mean this as a criticism or insult in any way, but I honestly don't know how "orthodox" or "Sunni" he really was when he died. Yes, he left the clear shirk of the Nation and was disillusioned by Elijah Muhammad's adultery but I don't know what beliefs he had in terms of Abu Bakr or Ali, in terms of the validity of hadith, following a madhab, finality of prophethood, etc. For all we know, Malcolm X might have become an Ahmadiyyah had he lived longer (after all, the Nation relied on Ahmadiyyah literature in addition to the writings of Elijah Muhammad) And yet, in spite of his ambiguous orthodoxy, Malcolm X is (and rightfully so) considered one of the most exemplary Muslims America has ever produced. The fact that he was an individual commited to one God and social justice trumps more pedantic concerns about theological correctness, at least in the grand scheme of things.