In a patriarchal society like that of ancient Greece, it would be pretty hard to have a play with a fearsome female villain like Clytemnestra and not have the issue of gender play a prominent role. At many points in Agamemnon, we hear characters utter stereotyped views about women, but it isn't clear how much Aeschylus endorses these. For example, the Chorus frequently remarks on how women are irrational and don't pay attention to the facts. The Chorus members intend this as a criticism of Clytemnestra, but do we really see her being irrational or making factual mistakes? Evil though it is, Clytemnestra's murder plot definitely required careful (i.e., rational) planning, and she was right about the signal fire from Troy, which the Chorus doubted. Also, the Chorus is majorly wrong in mistaking the appearance of Clytemnestra for what it really means, when they can't believe she will be Agamemnon's killer.
Clytemnestra's actions do, however bear out another cultural stereotype in the play: that women are untrustworthy. (Of course, it could also be said that Agamemnon is untrustworthy, since he sacrificed his own daughter.) At the end of the play, when the Chorus makes fun of Aegisthus by calling him a woman for not going to war and using deception to get back at Agamemnon, does this question or reinforce stereotypes?
The character of Clytemnestra reinforces gender stereotypes of women as untrustworthy.
Clytemnestra proves many of the Chorus's beliefs about women wrong.