A lot, as you've probably guessed, has changed in the last century. Back when Shaw wrote Pygmalion, women could not vote in the United Kingdom; in 1918 women over the age of 30 were given the right, and it took another ten years for all women to be given a voice. Shaw's depiction of women and attitudes toward them is impressively and sometimes confusingly varied. They are shown in conventional roles – as mothers and housekeepers – and as strong-willed and independent. The play pays special attention to the problem of women's "place" in society (or lack thereof), and Shaw offers no easy answers to the tough questions that arise.
In Pygmalion, Shaw portrays a society in transition, in which progressive notions of femininity clash with more established, traditional ideas about gender roles.
In asserting her independence from Higgins and the usual conventions regarding marriage, Eliza nonetheless ends up confirming established gender stereotypes.