Defining "key" social characteristics can turn out to be a bit on the tricky side.  It is difficult to create a hierarchy of such traits because in many complex social situations, they converge and interact against and within one another.  Certainly, racial/ ethnic, gender, and class based social characteristics are all highly relevant and can provide a great deal of thought which can be expressed through writing.  At the same time, you correctly point out religious or even national identity can also provide much in way of social characteristics which are very fluid and can be expressed in writing.  In the final analysis, it might not be your social characteristic, but the explanation and indepth analysis of it which might be the strongest for the writing.

Again, depending on what your topic or angle is, but another interesting topic to consider is race, especially given the dynamics of the 2008 election and the regions of the country with differing opinions on race.

You could also consider region as its own topic, as there is a distinct difference in culture and how culture is handed down generation to generation based on where you live in the country.  Compare West Virginia hill country to Boston to New Orleans to Beverly Hills.

For religion, look at the "Bible Belt" of southern states, Mormons in Utah, Latino Catholics in the Southwest, and Jews in New York.

I guess the question is what are you writing about?  Which characteristics are key cannot really be determined without knowing what you are talking about as an issue.

For example, if we are talking about political attitudes, gender is pretty important.  Women tend to vote differently from men and they tend to have different views on various issues.

When it comes to attitudes on gay rights, for example, age seems to be a very important variable.

So it will be hard for you to get a good answer unless you clarify the question.