No. The great majority of Muslims in Western countries want to live by their faith in private and to obey the law of the country, which Islam teaches them to do when they have been given safety and the right to practise. The Quran says there is no compulsion in religion.
The fuller answer
Islamic teaching asks Muslims to keep their agreements and to be loyal to the country in which they live in peace. The Prophet ﷺ sent some of his followers to live under a Christian king in Abyssinia, and they kept to the laws while freely practising their faith. Scholars have named this a covenant of security.
Some Muslim groups in some places do call for Islamic law in their own country, and Muslims disagree amongst themselves about it. But the idea that Muslims in the West want to force their rules on others is a fear that surveys of Muslim communities do not support.
There shall be no compulsion in [acceptance of] the religion. The right course has become clear from the wrong. So whoever disbelieves in Taghut and believes in Allah has grasped the most trustworthy handhold with no break in it. And Allah is Hearing and Knowing.
Allah does not forbid you from those who do not fight you because of religion and do not expel you from your homes - from being righteous toward them and acting justly toward them. Indeed, Allah loves those who act justly.
O you who have believed, fulfill [all] contracts. Lawful for you are the animals of grazing livestock except for that which is recited to you [in this Qur'an] - hunting not being permitted while you are in the state of ihram. Indeed, Allah ordains what He intends.
This answer follows the mainstream Sunni understanding and is general learning, not a fatwa. Where Muslims differ, the answer says so. Have a question of your own? Write to us.