Complex sentence: Progressives believed Prohibition would improve society as generally did women, southerners, those living in rural areas, and African Americans; however, a few exceptions, such as the Woman's Organization for Prohibition Reform, opposed it.
Split into simpler sentences: Progressives believed Prohibition would improve society, as generally did women, southerners, those living in rural areas, and African Americans. However, a few exceptions--such as the Woman's Organization for Prohibition Reform--opposed it.