A "green card" is a valid form of ID for a checkpoint today and there is no reason to suspect that anything will change between now and the full implementation of Real ID.
For all of the practical reasons above, e.g., losing an original is expensive, time-consuming, and stressful to replace, I would suggest obtaining any of the multiple Real ID-compliant forms of ID which ought to be readily available to you.
One of the reasons is not that some TSA Officer might reject it. On the off chance that this occurs, simply ask for a supervisor.