Millions of Moslems have had to leave their home countries like Syria and Lebanon to avoid being tortured and killed. When they left they took the same religion from whose zealots they were running, and set it up in their new homes, including the United States of America and Great Britain. They've moved into a lot of other countries as refugees too. A lot of these countries accept people who are refugees from oppression. They would not accept the deliberate moving of large masses of people who are faithful to the Taliban, Hamas, or any other such groups. They have accepted millions of refugees, who spread their religion through the areas that they are introduced to. Those refugees even maintain ties to terrorist organizations. Had they not been violently ejected from their countries of origin, Moslems would not have found so many homes where they could increase their numbers. Oppression actually works to increase the number of Moslems and the area that they occupy.
It's not quite the same. Some of this happened with the Puritans and maybe a few other splinter groups, but before, during, and after that time there were many deliberate invasions of the Americas by Christians in the name of God. I suppose that the Moslems have done that but I don't know. What I do know is that Moslems are establishing large presences in many nations as refugees who were taken in on compassionate grounds. I suppose they will take insult if I compare this to the tribes of Israel who were taken in by the Egyptians when their lands were taken by natural disaster. There was that Botany Bay business, too, so the Christians did stuff like that. They did also send a lot of "undesirables" to America to beat the natives down and then followed with the church ladies to take credit and take over. This was along with the primary thrust of the deliberate invasions.