E-martin makes an excellent point that the bias of the researcher should be recognized in each study. Sometimes the studies promote and reinforce negative attitudes. I think they can actually be damaging when they don't consider all factors involved when analyzing their data. For instance, the tons of research studies that will always show how blacks under-perform academically. Without pointing out researcher bias as well as going deeper with other factors, these studies tend to only scratch the surface of the problem, and I think they can be harmful and make discriminatory implications.
Subjectivity ends up being built in to almost all studies. Even when using statistical data and polling and other measures attempting to be objective, the design of a study, a poll or a questionaire will be determined according to certain preconceptions.
Maybe the best way to deal with subjectivity in the social sciences is to recocgnize bias within the hypothesis of a study, attempting to take the scientist's background and point of view into account in the design and context of the a study.
I am going to go out on a limb here and say no, objectivity is not possible. You can attempt to be objective. You can try really hard. However, there is quite a lot of emotion present in ANY type of research. People who think that quantitative research is objective because it is about numbers are just kidding themselves. There are still humans behind those numbers. Humans collected the data, wrote the research questions and so on. You can make numbers say whatever you want.
Complete objectivity is not possible because we all have biases that we bring to our research. In social sciences, the researcher must interpret the data they find. For example, if I want to research what causes kids to do badly in school, I have to look at all of the factors (sex, parents’ education, wealth, parenting styles, etc) and try to determine which is most important. Inevitably, my own biases will have an impact on me as I think about this issue. Therefore, it is much harder for a social scientist to be 100% objective than, say, a chemist.
In my opinion, it depends on what you mean by "objectivity." If the word denotes some degree to which a fact or truth is established, I'd say that it's dangerous to give up the idea of "objectivity" in any science. In fact, it's internally inconsistent. On the other hand, I wonder a lot about the "objectivity" of the social sciences, mostly because I'm not sure what they're based upon and because a lot of their work is inductive (which is fallible). I think that's a really hard question to determine.