I'm not a historian, but I'm a (white) Creole who's very interested in this kind of thing, so I'll give what I know in the hopes of guiding you in the right direction.

As you've pointed out, the stark black-white dichotomy, and the infamous one-drop rule, are Anglo-American concepts that did not exist in Louisiana prior to the Purchase (or, from a Creole perspective, the Sale). It was lawfully and informally imposed by white migrants from other parts of the still relatively new United States over a period of several decades.

You may not have intended this meaning, but I take slight issue with your grouping of Creoles and mulattos together. "Creole" was not, and never has been, a racial identity. It is not a racial categorization. Anyone who was natively born in Louisiana during the colonial period, or descended from the same, was Creole. Purely French, purely Spanish, purely German, purely African, partially mixed, largely mixed—totally irrelevant. PGT Beauregard and Kate Chopin are well known white Creoles, as is the French painter Edgar Degas (whose mother was a Louisiana-born Creole). Likewise, Beyoncé Knowles is a Creole of mixed race, as was Homer Plessy of Plessy v. Ferguson. Viewing the identity through a racial lens is a sign of Americanization.

The sad fact is that the Creoles of color were essentially not given much of a chance to resist. Some white Creoles tacitly supported their tactics, but not to any great extent, as their own personal interests demanded that they integrate with the white Americans. Having the advantage of superior education, however, allowed Creoles of color to at least attempt to defy the new status quo better than new freedmen in other parts of the American South, and indeed many effort to promote Civil Rights in the 1800s came from Creoles of color. But they were steadily disenfranchised thought the late nineteenth and early twentieth centuries.

This strategy partially had to do with the Anglo-American racial ideology, but it was also part of a concerted effort to Americanize a people who were potentially problematic. (This is why they took steps to stamp out the French language as well.) Educated gens de couleur libres—free people of color—posed a threat to the status quo in other parts of the South, as they essentially subverted American ideas of what people of African descent could and could not be allowed to do. And while no serious historian could claim that pre-American Louisiana was by any means a color-blind society, there is some historical evidence that suggests a certain amount of solidarity between Creoles of all racial backgrounds against Americans. After all, the Creoles spoke the same language (usually French) and practiced the same religion (Catholicism), neither of which the Americans did or even frankly approve of. The Comité des Citoyens, which encouraged Plessy to defy the law by sitting in a "white" train car, was a Creole organization that included whites and blacks alike.

This began to fall apart in the early 1900s, when white Creoles began to fear that, to their now-powerful American neighbors, that their Creole identity implied racial "impurity." They responded by arguing that only whites could truly be Creole (see the writings of Alcier Fortier and Charles Gayarré for prominent examples). Then, when this tactic failed, they responded by abandoning their Creole identities altogether. In the mid-1900s, when the Cajun-craze came about and everyone wanted to be Cajun, rural white Creoles essentially switched identities to one that was less racially ambiguous (so says historian Carl Brasseaux). This is why relatively few white people today claim to be Creole. But they are. In fact, all Cajuns are technically Creole according to the early definitions, and there is some evidence that at least certain Acadian descendants identified as such. It was a subcategory, not a distinction. If you read French, you might find this study interesting, wherein several white Creoles complain that their identity is being eroded by "Cadjins" (Trépanier, Cécyle. "The Cajunization of South Louisiana: Forging a Regional Identity." The Geographical Journal, Vol 157, No.2 (July 1991), pp 161-171.) Awareness of the original identity is slowly growing stronger, too, so there is perhaps a slow restoration going on.

So the ultimate answer to your question is: Americanization on a series of levels meant to weaken Louisiana's unique identity and thus its political power. This persisted until the 1960s, in fact, when national lawmaker expressed concern that Congressman Domengeaux's founding of CODOFIL (the Council for the Development of French in Louisiana) could fuel separatist discontent, such as the kind that was simmering in Québec. And if the French language were to have a major revival in Louisiana—which is possible, although not likely—such sentiment would very likely flare up again.

​

If you have any specific questions or want sources on any specific point, let me know and I will try to track them down for you.

EDIT: Thought I'd add that, while I have not experienced this myself, I have been told that, just as white Creoles were pressured to abandon the identity by white Americans, some black Creoles are dissuaded from identifying as such by certain non-Creole African Americans because they see it as a cop-out or denial of their "black" identity. Again, I have not experienced this myself because I am not of African descent, and I can't prove it because I have no scholarly resources that state it, but I do know Creoles of color who've said this, and you occasionally run across comments on Facebook or Youtube that seem to support this assertion. I thought I'd mention it because it shows that erosion of these identities continues even today, and not always in a political context.