There is an overlap between those who demand immigrants assimilate to mainstream American culture and those who resist having their children assimilate to mainstream American culture by either homeschooling them or sending them to private schools.
I’m not sure how many people fit into this overlap. I suspect it is a significant number. Whatever their numbers, they seem to be a disproportionately vocal demographic.
Their view appears hypocritical, but maybe there is a hidden consistency based on a false belief. These kind of people seem to think their minority culture, typically of right-wing fundamentalism, often of the rural South Bible Belt, is mainstream American culture.
They are so disconnected that they don’t realize they are disconnected. Instead, they project their disconnection onto others and seek to scapegoat them. In reality, most immigrants tend to be more demanding about their children assimilating than are native-born parents and also tend to take the American Dream more seriously.
If everyone home-schooled their children or sent them to private schools, then and only then would American-style assimilation fail. Public schools are the backbone of our shared culture and they have been for a very long time.
It is strange how people forget history. Right-wing fundamentalists were the biggest supporters who originally pushed for public schools, and a major reason they gave was to help the children of immigrants to assimilate. This same group now attacks public schools.