The Left regularly claims that the Right does not see nuance. So here we have a case where the Right, in fact, sees nuance: they are against illegal immigration but very much for legal immigration. But to the Left, that distinction somehow does not register. To them, the Right is anti-immigration. From George Will:
The problem of illegal immigration is inflaming Mahony, who strongly implies, as advocates for illegal immigrants often do, that any law intended to reduce such illegality is “anti-immigrant.” The implication is: Because most Americans believe such illegality should be reduced, most Americans are against immigrants. This slur is slain by abundant facts — polling data that show Americans simultaneously committed to controlling the nation’s southern border and to welcoming legal immigration.