I haven't been picking up sources (and don't know if I should bother, given that you don't seem to accept anything)
That's primarily an issue with the quality of your sources. So far you've largely relied on the right-wing media and commentators, very little with academic credence. When you have used reliable sources, you've tended to mis-represent them or draw conclusions from their statistics that aren't logically sound. But let's get back to the response at hand.
The general problem I'm seeing here is that a lot of people - even some critical of religion - are claiming that a Muslim majority in the UK wouldn't be harmful and they'd be OK with it.
Who is claiming this? It's fallacious anyway, as the very idea of a "Muslim majority UK" is utterly absurd and therefore represents little more than a hypothetical supposition. Where are you referring to as "here"? I hope it's not this thread, as that's a completely baffling misinterpretation of the views that have been expressed here.
and not only because of the fact that no Muslim-majority countries in the world have ever been able to establish a stable society with a good quality of life.
Well, this isn't factually accurate. Take Indonesia for example, which outranks many of its neighbours in the various freedom indices but is majority Muslim. There's also Northern Cyprus- again majority Muslim but ranking higher on many of the freedom indices than either Greece or Turkey. But even if we take the point that, proportionally, Muslim-majority nations are less likely than, say, Christian-majority nations in terms of freedom and stability, it still doesn't support the conclusion that the cause of this is Islam. Correlation does not equal causation.
Not to mention the religion's totalitarian approach to politics.
Disputed, this seems to be a point based on emotion and opinion rather than empiricism but let's come onto that in a bit.
Way I see it, it's possible to divide the Muslims into 3 groups. Group A openly supports global Islamization and is ready to do violent and radical deeds to achieve that. Group B are the silent supporters, who don't participate in anti-infidel violence, but still support the Islamization movement by, for example, voting for radical candidates in elections, or just generally assisting them behind the scenes. Group C are the moderates, who disagree with the 2 other groups.
The problem we have here is that we have no idea how many Muslims are true moderates and whether they're only pretending to appear more sympathetic to the Western crowd.
There have been numerous studies on the issue, actually. Every piece of independent research on the issue has come to the conclusion that anti-Western sentiment is purely a product of a very small minority who adhere to particular sects of Islam. As I pointed out before, you don't get extremist Sufis. You don't really get extremist Druze, or to be honest extremists in non-Takfir/Qutbist/Salafist schools of Sunni Islam. Or really that much Shia extremism- the major Shia terrorist organisations like Hezbollah aren't terrorist by virtue of their religion but are armed resistance movement to Western or Israeli interventionism and perceived expansionism, funded jointly by the Soviet Union and left-wing groups in Central and Southern Europe. There's no rational basis for assuming that all Muslims harbour these sentiments; to do so it simply discrimination. No different from me claiming that, because most Christians don't speak out against the actions of the kind of extremist who bombs abortion clinics or gay bars, they must be complicit.
The main problem I see here is that the Quran openly permits lying and deceiving infidels if it's beneficial to Islam's spreading. This is the main reason I have so little trust to the "moderates" - even to them, the Quran tends to be the highest authority, and only after that comes the law of the land. And if the moderates really are such a huge majority amongst Muslims, why aren't they expressing themselves more clearly? Why is the allegedly tiny minority comprising of radicals so loud? We can all wonder about that...
This is entirely dependent on what school of Islam they choose to follow. The Quran is the highest authority for all Muslims, yes, but each of the major and minor schools of Islam interprets it differently. There are numerous nations in which large Muslim populations live harmoniously alongside other religions- Benin, Ghana, Cyprus, Singapore. As for the question of why moderates aren't heard, this is simply explained by looking at the far right movement in Europe. Why is far-right extremism given so much coverage by national and international media when it finds support amongst such a small proportion of most populations? Simple- those who shout the loudest have the most attention payed to them. Compare with, say, fundamentalist Christianity in the US. Fundamentalism has come to characterise the American Christian Right over the last few decades and external observers lament this, even though in purely proportional terms these individuals don't make up a larger proportion of the population than they used to. Why do believers in conspiracy theories always insist on shouting their views from the rooftops? In absence of any reasonable discourse and intelligent discussion, people just raise their voices, and unfortunately the majority are either too ignorant or too poorly informed to understand that those who speak softly on a subject are usually the voices of intellectual authority.
With Islam still stuck in the 7th century, how can we expect that a Muslim majority wouldn't descend back to the Dark Ages and hold science back in order to islamize the entire continent?
I could say exactly the same about the fundamentalist Christian movement. They probably represent a larger proportion of active, self-described "Christian" religious believers in the US than Islamic extremists do Muslims in Europe, so surely the same argument applies to them? The simple fact of the matter, as just about anyone schooled on counter-radicalisation and counter-extremism, security studies and counter-terrorism studies will tell you, is that the media- particularly the right-wing media- has massively inflated the potential threat posed by Islamic extremism in Europe. More people have been killed and injured in the UK in the last 5 years by Republican paramilitary groups with a cumulative total of around 400 active members, than have Islamic extremists who by all accounts number in the low thousands- and by a factor of about 10. So tell me, statistically whose the bigger threat?
Unfortunately, given the fundies' nature, I doubt they'd want to be friends with the rest of the nation after becoming a majority.
Even if Muslims were to become a majority- and the've got a very, very long way to go as they represent on average about 6% of most European countries, who says they're the extremists? Non-sequitur argument.
And speaking of the Dark Ages, I, for sure, believe that no rational person would ever follow the Quran rather than a peer-reviewed textbook.
Which is all well and good, but the Quran isn't trying to be a scientific textbook. I've never met a Muslim of any kind who sees their religion as incompatible with science. I'm sure they exist but they certainly don't make a big song and dance about it like early-world creationists do. Not entirely sure what you're trying to get at here- you're either not making a point or it's another non-sequitur argument.
Back to Bilal Philips for one more comment... You do know that he's preaching hate towards infidels and wants them killed only because they don't share his faith? I'm pretty sure incitement to ethnic or racial hatred is a crime around here. So no, he doesn't exactly have the right to come here and say anything he wants.
I don't think I've ever heard Phillips directly call for the murder of, or violence against, others on the basis of their religion. He was very critical of Boko Haram and their attacks against the civilian population in Nigeria. He argued to justify suicide bombing in a strategic context, and also supported the notion of armed resistance against Western interventionism in the Arab world, but neither of those views constitute an incidement to ethnic or racial hatred. It's a fine line- on principle I don't disagree with the idea that he's a vile individual and a preacher of hate, but so are many people who speak for the European far right- the kind of people who blame fatal floods on the legalisation of gay marriage, or for that matter level unfounded allegations against Muslims purely on the basis of their religion.