Jake, wind your neck in. Considering Tower Hamlets, home to the East London Mosque, has so many problems (see original link), Em's musing - and she was musing rather than accusing - is perfectly reasonable. Why wouldn't moderate Muslims want to attempt to limit the damage done by extremists and bigots in their midst? If they want to live in peace with their non-Muslim neighbours, it seems a sensible thing to do.
Incidentally, the Blue Mosque in Istanbul is worth seeing, but I wouldn't make a special journey for it.