I have not heard a concrete answer (or even a generalized opinion) on whether gentiles can have a re-incarnation, despite reading that they do not (Minchas Yehuda by Rabbi Yehuda Hachayat). I know that there are sources that say that a gentile does not have as many layers of soul as a Jew, and also that a righteous gentile has a place in the world to come, but other than that nothing definitive.
I have emailed the Chabad "Ask the Rabbi" service and was told, in essence, that it is complicated and not to delve into it, which was not a satisfying answer to me.
The reason I am asking is because I enjoy learning from video lectures and many of the Rabbis and speakers I enjoy listening to tend to speak to both gentile and Jewish audiences , and they sometimes mention re-incarnation passively in the context of life circumstances, suffering etc. It's because they have both a gentile and Jewish audience that I ask, because I have seen cursory mentions in some places that gentiles sort of only have one go.
Like what about Esau. He was born to Isaac, and circumcised. So Jewish. Rejected his birthright, so became an Edomite. Then he reincarnates into a Jew, and this Jew becomes another religion. So in both cases, starts off Jewish, ends non-Jewish. Therefore, is this reincarnation of Esau considered evidence that non-Jews can reincarnate, or not? But the Nimrod example might be more clear cut
– ShipBuilding Mar 29 '22 at 10:45