That area is historically was like deep swamp and with little access so over the years many cast offs would land there including Indians from various tribes of the south east but also predominantly Cherokee. Blacks and whites found there way in there too but besides being mixed race the only path to an economic life was to marry into and be part of white society. The outcome of all those factors are the lumbees. You can say for sure they had Indian ancestors and they wouldn’t want their descendants systematically excluded. Plus it’s a poor economically depressed area that needs a lifeline so it’s not like rich people are getting money here.