They’re not diminishing themselves...they are preserving themselves. The many many Cherokees have and STILL mary Cherokees...THEY are the ones that should have the blood rights to vote on issues in their nation. Not a bunch of quad-breeds or sextant-breeds that have no interest or business within the Cherokee Nation.
My children still have interest in their inherited culture from their grandparents. But they don’t feel they have a right to interfere in the business of their kinsmen who actually live within the Nation and its laws.
Culture and sense of nation goes with personal political affiliation ~ not your genes.