I think she is often portrayed or joked about as unstable because she's a woman. She goes crazy because women can't handle stress, and so on. She is more sensitive than her husband. These are the stereotypes that lead people to make fun of Lady Macbeth.
While Lady Macbeth did not actually wield the knife that killed Duncan in his bed whiile in her home, it is pretty clear that she is capable of murder. The sight of blood, horrific to her husband, does not make her queasy or faint; she tells him a little water will get rid of it--and quit being such a baby about it. Lady Macbeth asks the gods to "unsex" her, giving her the constitution of a man who is capable of committing cruel acts without conscience.
One of the great ironies in the play, for me, happens the morning after it has been discovered that Duncan has been mudered. When Lady Macbeth feigns ignorance and asks innocently what has happened, Macduff says:
His words imply a sterotype of women as weak and fainting at the thought of gruesome things, which is certainly ironic given her role in the murder.
One stereotype we have is that any woman who wants power is in some way evil and "unfeminine." We see such women as unnatural because we believe that women should be retiring and deferential to men. This is often seen in the way that women in power (even today) are portrayed. Women who act in the same assertive ways as men do are often vilified.
You can argue that this is what happens to Lady Macbeth. She is a stereotyped character (you can argue) because she is woman who wants power so much that she goes completely overboard. The implication here is that a woman who wants power is flawed and unnatural and is therefore likely to go too far in pursuit of that power.
So, you can argue that Lady Macbeth is stereotyped because she conforms to our perceptions of what women who want power are like.
I think that there might be some real questioning about the nature of the question. I don't think that Shakespeare stereotypes her based on gender. Her presentation in the play is complex, as she represents both the most unholy of actions and the remourse and regret of someone who has understood the nature of personal sin. In this, she is complex and intricate, not a simplified stereotype based on gender. If there is a stereotype associated with Lady Macbeth, it might be developed by readers or critics who are so quick to associate her as the primary cause of the bloodshed in the drama. This view might be accurate to a certain extent, but fails to take into account two key points. The first is that Lady Macbeth might goad or galvanize her husband into action, but it is he who actually carries out the act and he who actually stands by it. At the same time, the gender stereotype of Lady Macbeth fails to accept that Macbeth, after a certain point, pretty much severs all communication with his wife. At a point in the narrative, he is on his own and his wife is no longer relevant to he or the defense of his throne. If this is the case, then she cannot be the cause of evil for she is no longer present in his calculations. He acts on his own or with the aid of the witches. It is here where the gender stereotype fails. Yet, some will continue with it because it is provides comfort to individuals in blaming Lady Macbeth as the source of all evil, as opposed to representing Macbeth's crimes as a continual representation of multiple and varied factors.
Although Lady Macbeth on the surface appears too strong for a women, especially in the society the play was written in, the interactions between her and Macbeth paint her character as that of a stereotypical wife; she is the one that makes the plans, and is practical steadfast one of the relationship, she also has the ability to persuade her husband - traits that stereotypically women have. The timing of her illness is also very noteable, as she becomes unstable as Macbeth pulls away from her, this links in with a quote actually from Romeo and Juliet made by Friar Laurence 'women may fall when there's no strength in men' which is what happens with Lady Macbeth (although Macbeth has just pulled his strength away from her). This shows the difference of when Lady Macbeth was the dominat one in the relationship at the start, as she carried on to support Macbeth and, arguably, everything she does is for him.Overall this shows that despite her coming across as unconventional for the society she was written in there are aspects of her that are most certainly stereotypically womanly.