Mexicans were the largest group of immigrants in the US military back then. But there were also significant numbers of Russian Jews, Poles, Ukranians and other Eastern European immigrants, as well as a few from everywhere else. I saw Chinese immigrants in basic, but never in VietNam. I assume it was considered too sensitive to send them to VietNam... it might make the ChiComs angry and get more involved than they already were.
Toward the end of my army career I met a medic who was an immigrant from Nigeria. I asked what had prompted him to join the army. He replied, "This great country has been good to me, and this is my way of paying her back."