The play does not merely reinforce stereotypes. It shows how women can break through stereotypes. I would caution, however, against the false dichotomy of either so-called strong females characters or a sexist narrative. Women in real life are neither strong nor weak in every cause, just as men in real life are neither strong nor weak. Humans have both good and bad qualities and there are some people who are stronger than others. Shakespeare presents a realistic cast of characters with a different array of realistic strengths and weaknesses. I would argue this is actually more of a break from convention than simply preventing a series of women who confirm to the strong/weak binary.
The fairy queen, for instance, is generally a very strong character. She is in a position of power and she disobeys her husband. She becomes a fool, however, when the love spell enamors her with Bottom. This is not a reinforcement of stereotypes. She is still a powerful and strong woman. Shakespeare is merely demonstrating how strong people are often foolish in the face of love, even when that love that is fading and superficial. This is realistic of human beings, whether these humans are male or female. Note that the male characters of the play are also swayed by the spell. No character is immune from the charms of love.
Shakespeare presents many kinds of women: Helena, who has a stereotypical pining for her lover, Titania, a powerful woman in conflict with her husband, Hippolyta, a strong, free woman in love with a man of order, etc... This depiction of women as human beings, with the same flaws and strength as men, is the very sort of force that breaks stereotypes in literature. Strong female characters alone are often as foolish as weak characters alone; both demonstrate that women exist on a binary, unlike the more complex male characters. Complexity breaks convention, not strength.