[P]eople with higher levels of education and occupational skills are more likely to favor immigration regardless of the skill attributes of the immigrants in question. Across Europe, higher education and higher skills mean more support for all types of immigrants. These relationships are almost identical among individuals in the labor force (i.e., those competing for jobs) and those not in the labor force.
As a professor, I work in one of the few labor markets that is almost totally open to foreign competition. How often do you think I've heard an American professor grumble that foreign Ph.D.s "Are taking our jobs!"? Try never.
P.S. For more on Hainmueller and Hiscox's work, see here.