Squonk seems to think that (1) Islam has serious and deep-seated theological problems with divinely-sanctioned violence and repression,
Not all of its denominations: I don't know about alawites, for example. But sunnis and most important shia denominations do. That doesn't mean each person of those denominations has them personally.
(2) problems that are more relevant to Islam than their counterparts are to the other Abrahamic religions
than christianity, I don't know about judaism. It doesn't mean christianity doesn't have more problems than islam in other fields.
because a prominent section of the Islamic community draw on them to institute reprehensible practices.
draw on what?
because the literal meaning of some coranic verses and hadiths is violent, and for centuries that was the official interpretation of them in most islamic denominations; these interpretations are still legal today, although if there's some new judgement in this subject, one may chose between the old and the new interpretation. Also, currently the law is mostly about taqlid, that is repeating what was already said by great jurists of yore, and anyway I honestly doubt that one can come up with an interpretation that strays much from the literal meaning.
(3) the whole Islamic community has the responsibility to resolve these problems because they originate from the same texts that all Muslims hold as sacred.
I'm not sure Squonk has enough credibility to say this convincingly, as I have seen no indication that he is well-versed in Islamic theology. Just because you can and have read holy texts doesn't make you an authority on the theological problems arising from them, since you are probably not familiar with the body of the theological debate concerning them.
I am doctoral student in arabic studies. That doesn't make me a great buff in islamic theology and jurisprudence, as my sphere of interest is classical history of islam, but it shows I have some basic knowledge in this subject. What qualifications do you have?
I'm leery about the second point because I agree with what Traitorfish has said. It doesn't matter if I personally have no firm grasp on what the essence of Islam is. I can simply rely on the evidence that there is a vast number of moderate Muslims who do not share the views of the more extreme. Since I don't think I can presume to say that the moderates do not understand the essence of their religion, I am therefore satisfied that the essence of Islam must be benign and compatible enough with modern values.
"I know nothing on this subject, but I'm sure I'm right"
your thinking rests on several assertions. I will discuss some of them.
Firstly, you do disagree with the thought that one may judge a religion by the actions of it's adherents, when it's about bad behaviour; but when it comes to "good" behaviour, you have no doubt that one may judge islam by it. You should make up your mind. You, and earlier others, were molesting me to show the quotes of Al-Qur'an etc that support violent actions; when I did, you demanded from me to show a link between these quotes and behaviour of some. Yet, making an analogical claim, but to the contrary, you didn't provide neither quotes of Al-Qur'an nor examples of practical application.
I don't expect you to, as I know you have little knowledge in this subject and apparent disability preventing you from using google (or whatever), but I'm informing you that there are such quotes and there are examples of their practical application. They concern only a couple of problems, though, mostly well treatment of dhimmis, and the dhimmi status is result of weighting the "bad quotes" against the "good" ones.
Secondly, certainly I agree that there is evidence that the vast number, bah, I dare to say almost all of muslims don't act as the extremists do. That doesn't mean that all of those that don't act as the extremist do disagree with them, though. Your assertion is that lack of action equals a conviction contrary to this action, which is wrong. Someone can agree with extremists in part or plainly, but that doesn't mean he will act as the extremists do. Also, he simply doesn't have to ask himself the questions the extremists do. I think that most people don't pose these questions to themselves, or avoid answering them, being busy with everyday life. I think it's also possible that extremists, active extremists, may be people of specific mental condition, people unusually sensitive for dissonances in their worldview. But it's just a thought. And another thing: some do not have a possibility to express their extremist views.
In general, I'm convinced that a group of people who - potentially or consciously - agrees with extremists, although does not act as they do, exists. But its number may vary from very significant to next to none depending on a country. If one found such a person among polish Tatars, I'd be surprised. But if this number wasn't significant in, say, Yemen, I'd be surprised as well.
I do believe that there's a significant number of more or less moderate muslims, not only in actions, but also in thinking. But it's not self-evident and if you want to use it as a proof for anything, I urge you to find some polls on this subject.
Your second assertion is that the essence of islam is something that is, or is not, responsible for the extremism. Again, one would have to define what this essence is. I already stated what I believe to be the very essence of islamic religion and that that's not where's the problem.
Your third assertion is that one may judge a religion only by its essence. We've already discussed about it.
Your fourth assertion is that the moderates understand (the essence of) their religion, and that they act according to it. If one defines the essence as I did, I see no bigger problem. But one may argue that the moderates indeed do not understand the essence of their religion, as they change the established understanding of this religion to fit some un-islamic worldview. If someone views shari'a as part of essence of islamic religion, he may claim that they're not muslim anymore, while claiming they are, which would mean that modernists, in the eyes of the traditionalists, do not understand the essence of the religion.
Also, moderates may be treaten as people well aware of that shari'a is part of essence of islam, but wanting to change it, disregard it anyway. That'd make them so-called hipocrites, munafiqun.
In addition, I'm also fairly skeptical of fetishising religion and ascribing to it some powerful motivational influence that is independent of human will. And therefore I believe that problems stem first and foremost from the human actors who generate and carry out whatever conception they have of their faith. But that's just me being Marxist and non-theistic.
I will answer you with an (not very precise) quote of Marx, which I used in my thesis: it's singular people that create history, but never alone, but in the circumstances they are provided with. Human actors think for themselves, but it'd be silly to ignore the cultural influence on them. And, being even more precise, a religious person may think for his own, but he has some axioms delivered by his religion. Of course, it is different if one person is laicised and individualised, when his "religion" is more a matter of a cultural tradition, when he doesn't really devote himself to any particular denomination's beliefs and choses out of his holy books and his religion's teaching what he pleases. Then it's different, but it's a very modern, fresh phenomenom that didn't reach the muslim world in a way that could be compared to the progress it's made, say, in Europe.
Nowdays I'm pretty sure one could find a person who's against the Trinity and cult of saints, is all for abortion, doesn't consider letters of St Paul as part of New Testament, denies papal authority in the church, etc, but still would say he's a catholic, as he was baptised in this church.
Well, I'm not sure if such a person is a catholic nor if he understands the concept of catholicism.