Immigration is not leftist, it degrades value of labor. It's liberal policy - in the US this is conflated with left, but elsewhere liberal stands for individualist policies, while left is more or less socialist, the exact opposite.
Certain kinds of leftist are anti-immigration. But anarchists and those in favor of international communism are aggressively (sometimes militantly) opposed to the concept of national borders or any meaningful restrictions on the movements of people.
