Typical soapbox preaching this week.
Assertion: Some people want to edit out this haftarah (presumably because it talks about a woman singing, or being a judge, or a prophet, or some made-up reason).
Fact: No one wants to edit out this haftarah. Everyone from Modern Orthodox to Chareidi/Yeshivish/right wing/black hat reads it.
Assertion: Devorah judge, Devorah prophetess, women singing, back of bus, women do lots of things in this day and age, yada yada yada.
Fact: Devorah was a prophetess, no one has any problem with that. The navi also states that she judged Israel at that time. The question is, how does that comport with halacha? The generally accepted halachic opinion is that a woman cannot be a judge. Since we learn from verses in the Torah that a woman can't be a witness (in a trial where witnesses are required, not just a witness to clarify facts), and anyone who is prohibited from being a witness is prohibited from being a judge, a woman can't be a judge. Therefore, the usual explanation is that Devorah did not judge in the usual sense, but rather, that people sought her sage advice on a non-binding basis, or that she "judged" via her prophetic abilities, or some other explanation along those lines. There is a minority opinion that a woman is allowed to be a judge even though she may not be a witness, and therefore according to that opinion there would be no problem with Devorah being a judge even with the usual understanding of the term.
Men and women can't sing together. Men can't listen to women singing. That's the basic halacha. There are exceptions according to certain opinions, such as, maybe, allowing a group of men and women to sing zemirot together if we are afraid that discouraging the women from singing will turn them off to Judaism. And there may be an exception for men to listen to a group of women singing, because no one voice is heard clearly, or an exception for hearing a woman without seeing her, such as on a recording. But the basic halacha is as articulated above; the Talmud clearly states that a woman's singing voice is in the same category as certain parts of her body--private, and not to be seen by men. So in the haftarah, Devorah and Barak sang separately, just as in the parasha, where it states clearly that the men and women sang separately following the miracle at the sea.
Halacha is eternal and unchanging. Sometimes the application of the law may change, when the halacha itself says it depends on the situation. But other times it doesn't. In this case, it doesn't really matter if women are doctors or lawyers, or if the world has become more "egalitarian", etc.-- men still can't listen to them sing. It's no different than if the whole world eats pork--Jews still can't eat pork; or if all women in the world wear sleeveless dresses--Jewish women still can't wear sleeveless dresses. Even if Jewish women are out in the workplace and have significant roles in society and non-Jewish society says there are no differences between men and women--halacha is what halacha is. And this dovetails nicely with what we've said in the past--we don't look to non-Jewish, secular society to tell us what's right and wrong and how we should behave, because those "rules" were made up by human beings. We look to Torah, which is the set of rules promulgated by God.