Yeah --- well WHICH labor union??? The hispanic United Farm Workers Union and Cesar Chavez. You can't really blame them because they knew that unlimited immigration was just to keep their wages dirt low. Wages and benefits only go up when there is a demand and competition for labor --- or by labor unions and strikes.
Nope, it was and is an article of faith with almost all labor unions that unfettered immigration is bad for the American labor movement because it will depress jobs.
The farm workers union wasn't even formed back then. But by the time Chanvez came along, they were too close to the immigrants to take a stand against them.