It is almost impossible to renounce your US citizenship that’s the problem. However, I think it is far more relaxing for green card holders.

Go see the following in Wiki for quick reference about US citizenships:

Perez vs. Brownell

Afroyim v. Rusk (over-turned Perez vs. Brownell)

Vance v. Terrazas (introduce preponderance of evidence which make it kind of hard to get rid of US citizenships).

Three ruling by the United States Supreme Courts.