It's probably true that many Islamists hate western culture, it's probably true that they want to influence it and control it, as do many politicians.
All sorts of different factions want to influence politics. It isn't the monopoly of Muslims (nor "Islamists" which is a form of Islam encapsulated within a political system).
In fact I'd suggest that Muslims are rather late to the party, in the UK, and other western nations, in so far as the beneficial effects of influencing politics.
There is much historical evidence of different factions influencing poliitcs since the 19 century, and before.
I don't see any historical evidence of Muslims (nor Islamists, which is far too recent a "group identity") getting in on that action.
Islamists tend to create a political system within a state based on Islam, rather than try to influence other political systems.
Is it true that Islamists hate western culture? From my perspective it seems pretty much a mutual hatred, born out of and perpetuated by comments such as yours, and others.
Except that western nations try to interfere in "Islamist" political systems
¹, whereas Islamists political systems want to mind their own buisness and just get on with life.
¹ There's been many historical instances of western nations influencing or causing "regime" change, etc in Islamic countries.
I've yet to hear of Islam influencing or causing a "regime" change of a western nation., other than a reversal of western nations' "puppet governments" in previous Islamic countries.
Such implementation of "puppet governments" and subsequent reversals tend to cause a more radical Islamic government than the previously ousted ones. Sometimes with specific stated aims of opposition for western nations. (I would include Israel in the bracket of 'western nations').
So the western influence or installation of puppet governments has merely caused a widening separation of the positions of the various governments and cultures.
