A case involving descendants of Cherokee Freedman is being decided. I can't speak to that case, I do not know enough about the Cherokee, but I can address the question as it applies to the Choctaw.
As like most matriarchal tribes, the Choctaw citizenship guidelines were always that you take the tribe of the mother. The only exception to this occurred when the tribe accepted children of Choctaw men and white woman, but only if they were married. Before the Dawes act, before registration, some Choctaw men adopted their illegitimate children to make them tribal members. There are children of Choctaw men with white woman who weren't married who were denied membership to the nation during the Dawes enrollment.
But what is the freedman question? First you have to understand how it came to be. During the civil war, most of the Choctaw, Cherokee, Chickasaw, and other tribes who were in what is now Oklahoma supported the south. Slavery was as prominent within those nations as without, and some economists suggested that as farmers with slaves, the Choctaw were more successful. When the Civil War ended, the nations had to agree to a new treaty with the United States. In a large part, they were penalized heavily for their participation. One of the stipulations of the treaty of 1866 was that they must allow all former slaves to be full members with equal rights in their nation.
It's ironic because the United States didn't offer the full equality to their former slaves in the south until the Civil rights movement, but I digress. So the former slaves were given a choice of remaining or leaving. Those that remained were called freedman. Now comes the tricky part. There is without a doubt many descendants of freedman who are part Choctaw who are on the freedman rolls. Dawes testimony for the freedman was at times as contested for the freedman as much, if not more, than some of the applicants of the Choctaw. The question was whether the applicant was a freedman or a statesman (meaning born outside the Choctaw nation).
Not every freedman is not on the Choctaw rolls though, because it comes down to the Choctaw tradition. You take the tribe of your mother. So if you take the tribe of your mother, and your father was Choctaw, but your mother was a freedman, you are on the freedman rolls. If your mother was Choctaw, you are on the Choctaw rolls. It is understandable that descendants who were as much as half Choctaw to begin with may resent the difference in the status on the Dawes, which ultimately effects their rights within the tribe today. However, I would argue, that if they were to state all descendants of Freedman be given equal rights to their respective nation, then all descendants of unmarried women who were denied because their parents weren't married, even though testimony stated their father was Choctaw should be included.
That would open up a hornets nest that won't happen. The court may decide that the Cherokee nation must give equal status to the Freedman descendants, we will have to wait and see. It's a tricky question, because, while many were in fact part native, many were not. I can understand how from some people's standpoint, despite living in the nation, you don't carry the genes of the nation, you don't belong. Yet, it was never right to deny those that had native blood because it belonged to their father and not their mother. Ultimately, it's not an easy issue, and I don't know that there is an easy answer.