As US is becoming less Europeanized, less Anglo, less liberal, through the large scale population replacement, you yourself will get to experience what it’s like to live in a society that values the liberal values much less than the people who founded and built this country.
Liberal values developed over time in course of which many tears were shed and much blood was spilled. In Europe and also here. [In other words, not 'innate' to the Europeans.]
I think your prognosis (which comes across as fear actually) may come to pass, but it will not be because US population is no longer primarily of European stock (some word!)
The primary driver has always been and remains culture. And culture in our age is an industry. And industry is subject to law & market. Liberal values are eroded because of the cultural content that undermine its validity and appeal. Non-Europeans will respond, I assure you, just as readily to formative cultural forces that engender an appreciation for liberal values, as do their "Anglo" fellow citizens. Likewise, both Anglos and the rest of us will also respond accordingly to cultural forces that are otherwise.