I think you're making the mistake of applying the general rules about race in the US -- that "one drop" of African blood was sufficient to be lumped in the out-group -- to New Orleans, which has its own unique cultural history. Having been a French & Spanish colony prior to the Louisiana Purchase (and then having a fresh influx from Haiti following its revolution), the region's attitudes towards race much more reflected those more nuanced approaches rather than the absolutist strictures which dominated in the rest of the United States. Instead of a White/Black dichotomy, the substantial population of gens de couleur libres in New Orleans (many of them mixed-race) enjoyed a more liberated and respected social status relative to people of African descent in other parts of the US.

John Blasingame's seminal 1973 text, Black in New Orleans, 1860-1880, obviously focuses on the post-war period, but does go into discussion of the antebellum racial system of New Orleans as well. Part of this system was recognizing a distinction between those who were simply free blacks, and those people of color who were a part of the more incremental racial system of France. Discussing the post-war period, he writes:

The free mulatto was French in thought, language, and culture while the black freedman was English-speaking and Afro-American in culture.

And Blasingame also notes economic divisions, not just cultural, separated these groups, writing:

Before the war mulattoes had become skilled craftsmen, and after the war they continued to dominate certain trades to the exclusion of the black freedmen, who had learned few skills in slavery. As a result of historical developments, most of the educated, refined, wealthy, and skilled Negroes in New Orleans were mulattoes, and, just as most men who are differentiated from the mass by these qualities have done, they formed associations among their own kind.

One of the more interesting aspects of the racial fluidity in early New Orleans was the practice of plaçage, wherein free women of color would becomes the mistresses of wealthy white men in order to garner benefits for them and for the children that would result from basically becoming the mistress of these men. Certain events in New Orleans, colloquially termed "Quadroon Balls," while not so formalized as the name implies, would provide opportunities for such arrangements. While not necessarily restricted to 1/4 African women, there was an emphasis on more European-appearing women, as an early and distinct form of colorism. To return to Blasingame, he notes that the patronage the mixed race children was vital to supporting the mulatto class as distinct and distinctly privileged as compared to free blacks.

A quick look shows that the Benjamin January novels are set in 1830s New Orleans, which is a bit of an inflection point. Sumpter (2008) (among others) puts forth the argument that it was during this decade that the older (Spanish/French) social system of gradations in racial hierarchy began to break down under increasing immigration to New Orleans from both Europeans (particularly Irish and German) and Americans from other regions who did not have the cultural background to understand the nuances of this system. The racial caste system of New Orleans, under this pressure and from increasing anxiety about race by American whites in general during the 1830s, thus began to resemble less that of pre-revolution Haiti or Spanish colonies, but the rest of America. Fisher (1969) likewise sees the decades leading up to the Civil War as a time when racial lines in New Orleans moved towards recognizing a more strict and legal segregation between white and blacks, with no in-between for a creole third race.

So, to answer your question directly, the racial categorizations you list were important to all New Orleanians, because they reflected the racial hierarchy and society of the time. Mixed-race people formed, in the early 19th Century, existed in a socially recognized in-between status which did not really exist in other part of the US at the time. The creole class of New Orleans were a racial group distinct from the "lower" blacks, and could and did identify more with white society. Increasing white immigration to the city, the end of slavery, and the passage of Jim Crow laws would all be factors in blurring the lines between Creoles and the Free Blacks. (There's actually an interesting hypothesis about how Jim Crow laws led to the development of Jazz, but that's getting far afield.) Prior to those events though, being a mulatto or a quadroon, or other person of known or apparent mixed African/European ancestry, meant being able to tap into a social class which, while it was definitely subordinate to white, was noted as distinct from blacks. It's no coincidence that Louisiana was home to a number of "Black" (i.e., mixed race) slaveowners, who were not simply purchasing their own family members, but exploiting African descended peoples similar to white slave owners in other parts of America. Henry Louis Gates compiled a list of such slave owners for an article he wrote for The Root; it is not a coincidence that the majority of names listed have French surnames.

Anyways, are the books any good?