Another way to put it: Muslims long ago realized (and it's more or less enshrined in the Koran-Sunna) that unless Islam takes over the culture, Islam will never quite have the power and dominance it deserves to have. Hitler and his ideological henchmen also realized this, and they created a Nazi culture, replete with symbolisms, new holidays, social gatherings, a new popular literature, a cinema, a new myth. But even what the Nazis managed to do pales in comparison with the depth and breadth of the Islamic Borg-like replacement of human culture with its new inhuman totalitarian culture. (I think this is one reason why Hitler and other Nazis admired Islam: they saw through the surface claptrap of its "religion" to its essence: a powerful totalitarianism both of society and of the brainwashed mind: doubly totalitarian, as Bousquet put it.)
Secularism: The Neutral Umbrella
A reader in the comments thread of a recent Jihad Watch article on honor killings in India made, with apposite economy of words, a very useful point to another reader's reflex spasm about how other aspects of "culture" (such as the Hindu caste system) may have diluted this Islamic honor killing: