That (conspiracy) theory pertains specifically to France, and Europe more generally w.r.t. Muslim immigration. It gets mentioned over here but it’s not a US thing.
It's metastasized and is very much a US thing, now. It hearkens back to the old white supremacist belief that Jewish elites are hoodwinking white people/culture/etc and replacing them with black people/culture/etc, for example. Similarly shaped ideas existed for hundreds of years in the US.