In the character of Beneatha we see a direct opposition of "assimilationism" to "Pan-Africanism" and this is the fundamental conflict for Beneatha.
She seeks self-respect through education primarily, which is not necessarily admired by the whole family, and she also looks for a positive self-image in connecting to Africa.
These two paths to a position of self-respect represent Beneatha's division from her family, which is a generational one. She cannot live without an identity that uplifts her, regardless of how often she is told that she should "accept her position" as a woman and a disempowered minority.
One thing that characterizes Beneatha is the self-detrimental ease with which she gives into external influence. I'm thinking in particular of Agasai's influence, which is very close to (if not actually) manipulation. Under Agasai's influence, Beneatha comes to represent Afrocentricity, which ironically takes her from her contemporary roots in her parents' and George's preferred path of assimilation.
I agree that Beneatha is torn between these two philosophies. While she presumably spends her life before meeting Asagai as an assimilationist, she does not become completely comfortable with her Afrocentricity, either. Beneatha is rather discontent in both worlds, and I suppose the statement Hansberry is making is that there is a balance to be had between the two extremes.
I agree with post #3. Beneatha is a preposition! She is truly caught "in between" her two worlds and is trying to find her way in one or both (indicated by George Murchison, her conventional and boring boyfriend and Joseph Asagai, her exciting and Nigerian boyfriend). However, she consistently makes remarks about how she is prevented from succeeding. She is "beneath" white society because of her skin color; she is "behind" everyone else in the family--especially Walter who is not only the older sibling, but also male, and in her eyes he gets more out of life and Mama; she feels "next to" Asagai, but even he wants to make her his wife (wihich is not necessarily equality) when she finds out the money which would help her become a doctor is gone.
I think that Beneatha represents the struggle between Afrocentrism and assimilation within her generation. While, yes, she does follow Asagai's advice about her hair, clothing, and even her future, she also begins the play by being quite assimilated into traditional American culture. One wonders if she would have been so Afrocentric if she had not met Asagai.
What is most significant about Beneatha is that like many young African-Americans in 1950s Chicago, she is torn between new found freedom (She has so many choices for hobbies and college majors, that she finds it difficult to choose among them.) and a sense of obligation to help African Americans find their identity, whether that be through participation in a Back-to-Africa-type movement or taking over what were considered traditionally white male roles (doctors, etc.).
Hansberry seems to use Beneatha's character to demonstrate that one can be an individual while embracing new ways of thinking such as Afrocentrism.
Quite clearly, Beneatha, through her friendship with Asagai, progressively seems to embrace more of her African roots and oppose assimilationists, such as George Murchison. Most obviously this is shown by the way in which Beneatha choses to wear her natural hairstyle, rather than straightening it. Note the response that this receives from George Murchison, who doesn't want to take her out looking like that. This however is what Asagai prompted her to do, as he pointed out the irony that her natural hairstyle is not accepted in society.