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You say you've identified specific types of immigrants that are incompatible with western liberal values. Who are they and how do you know?
That said, culture is strong and it's even stronger in the internet era, especially for large groups of individuals. It's extremely hard to bend or break it.
To that point, there is a great book, Armies of Sand, that talks about a concept called the culturally regular individual.
And the book makes a decent point that the culturally regular person from a specific culture is probably a distant match to Western ideals. And that distant culture has quite bad results in many areas we would consider important for modern society: education, research, industrial output.
I'll let you research more on this topic.