Sorry to be late with my reply, SP.
Personally I am rather cautious about analysing opinion polls, SP, especially those with low samples (1000 in the case of the Channel 4's Muslim attitudes survey I was citing). (This may or may not be connected to the fact that I spent over thirty years writing software for the market research industry.) A quick remark before I say why I don't share your optimism. The question asked in the British attitudes survey wasn't the same as that asked in the Muslim one. Basically the latter asked: should it be legal? while the British one asked: is it a sin? It is not inconsistent to disapprove of homosexuality while supporting its decriminalisation. I can't remember great outrage at the time of the Wolfenden report and the subsequent repeal of punitive laws against homosexuality, although it's possible I wasn't paying sufficient attention.
Let's forget the survey. My view until quite recently (far later than 9/11, in fact) was exactly the same as yours. While it was obvious that the Muslim community was causing more than its fair share of nuisance, I thought I could understand this in terms of cultural background and ignorance. What Muslim girl, I asked myself, would want to conform to the traditional norms about modest dress and mingling with the opposite sex when her non-Muslim school friends were buying sexy frocks, going to discos and meeting boys?
Since then I've changed my mind, not just because of what I've seen, but because of what I've learnt. These are what I see as the main barriers to assimilation of our (and Europe's) Muslim populations:
1. The nature of Islam itself: in its raw form it's a totalitarian ideology with a commitment to the subjection of non-believers
2. The rising number of Muslims committed to that raw form of Islam, which can be seen in political shifts in countries like Turkey, Indonesia and Malaysia which not long ago were seen as fairly secular and open, but also in Western-born Muslims who are asserting their Muslim identity (from girls wearing hijabs to boys joining ISIS).
3. The type of Islam taught in most British mosques (mainly Deobandi)and where most of the the imams come from (you've guessed it - the "less liberal" countries)
4. The rapid increase of the Muslim population caused by high birth-rates and immigration
5. The reinforcement of traditional Islamic values caused by immigration from the "less liberal" countries, and (in the UK's case) the widespread practice of first-cousin marriage wherein spouses are often acquired from the ancestral country (Maybe as many as 70% of Bradford's Muslims are married to first-cousins!).
6. The willingness of the West to accommodate a seemingly endless stream of Muslim demands (in the name of "social cohesion" or whatever) which means that in many ways (not all trivial - in fact NONE so) the majority are the ones doing the adjusting.