Limitations of "Green" Cards
My airline also has AMC (Air Mobility Command) contract flights. As a result, many of our non citizen junior pilots get to fly "senior" trips, (back at home in a day or two) and some senior citizen pilots get stuck flying AMC trips on the other side of the World, having to live out of a suitcase for a month. It has also become a scheduling problem, severely impacting seniority. As a result, the company will no longer hire non citizens.
"Green" card holders (Legal Aliens) have a right to live and to work in the country, but obviously they don't have "full rights" for every job. But they have a right to apply for citizenship!