If they want a Racial Constitution, then yes- Americans will have a problem with that.
The “ethnic” and “race” tests for land ownership are definitely problematic, and for the most part, even though we haven’t formalized anything with the U.S. to have status similar to the Native Americans, we would like Americans to think of those lands and the territory in terms similar to one of the Reserves, at least until the territory decides on a direction.
It is normal for an unincorporated territory to not have the full letter of the U.S. Constitution applied, and there is no time limit or deadline for such territories to make a choice. Congress, however, could mandate one.