Are you familiar with https://medium.com/incerto/the-most-intolerant-wins-the-dict... ?
This is a good example of how relatively small populations can have huge cultural effects.
Another example is how migrants from Islamic countries can carry out terrorist attacks and completely change European and American culture for the worse. The loss of American travel culture post 9/11 is tragic, and I can't think of a better word to describe it than "erasure".
Paris is now building a wall around the Eiffel Tower, thanks entirely to recent massacres committed by strongly religious immigrants for religious reasons.
Heavily Muslim neighborhoods in the U.K. have volunteer "sharia police" that harass women for dressing "immodestly".
Swedish officials removed traditional Christmas displays from Muslim areas, and then blamed the structural integrity of lamp posts (yes, really) when asked why.
Cultural erasure doesn't take a huge influx of people; it just takes a small population with aggressively viral cultural memes and a host culture with insufficient memetic defenses.
But, of course, I must be a racist for preferring European culture over throwing gays off buildings, women being unable to drive or show their faces, etc. etc.