There are some definite specific experiences reflected in Hansberry's work. The exploration of what it means to be poor and to be of color in the 1960s and 1970s are both brought out in the play. Additionally, what it means to be a part of a community and then seek to break from it is another specific experience in the African- American predicament. However, there are some levels of universality that are present in the drama. What it means to have dreams and to pursue them, as well as what it means to be crushed by the weight of those dreams are all universal experiences that individuals of different contexts all experience in their own way. At the same time, the exploration of bonds of loyalty to community and to self, and where there might be conflict in upholding both is another element that is explored in a specific context, but holds universal application.
I think it is a little of both. This play was written prior to the 1960s Civil Rights Movement. Many of the injustices that prompted this movement have been addressed in our current society because the laws have been changed (the amendments to the Constitution). So, legally, there are no more integrated schools, whites only sections on buses, whites only drinking fountins, Jim Crow Laws, and that sort of thing, but to think that we no longer have racism in this country is sadly, incorrect. Racism is a universal theme, and racism still exists. Civil Rights is still a concern, but not in the same way that it was in this play. It is more specific to a time and place in this play.
The broader issues of prejudice and tolerance are specific to the events in the play, but these issues are universal. We still have prejudice in the United States, not only against African-Americans, but against other races as well. Also, there is reverse prejudice and intolerance against whites by minority races. However, we DO have an African-American president today, so we've come quite a way.
The American Dream of owning one's own home, getting a college education, becoming a doctor are still universal concerns in the United States. This is a dream of all Americans, no matter what their ethnicity or mother country. When people come to the United States and become citizens, they are Americans.
Gender issues can either be specific or universal. Certainly during the time period of this play, they are more time-specific, but they have not gone away in modern times -- just taken on a new face. This play also predated the Women's Liberation Movement, so the women in the play are subservient to the men, which is not so much the case today in the United States. However, in some U.S. immigrant cultures, we still have the same sex roles as in this play. Although women have made inroads into the professions and business, there is still a "glass ceiling" which makes it harder for women to get the same pay and prestige as men.
So, a mixture. Read about it here on eNotes and see if you agree.