Oh, he absolutely was for women's rights. The man was quite progressive. If you were to read the plays like As You Like It or Twelfth Night and see the way he places women in these positions of dominance by making them men, you could make the correlation. Those are always funny, though. In the 1600s, women couldn't be onstage at all, so their parts were played by young men. So in a play about a cross dressing woman, you'd be seeing a young man playing a woman who is playing a man. Then in these plays, the women playing men then act like women to present certain concepts to the men in the play, like in AYLI where the woman is pretending to play herself. Suddenly you have a young man playing a woman who is playing a man who is acting like a woman. Confused, yet?
Also, the way that most of the women are dominant in many of the plays (Lady Macbeth basically makes Macbeth; Love's Labour's Lost houses a multitude of brilliant women, etc...), it's obvious that he felt the power of women goes far beyond aesthetic beauty.