This is the defintion of sexism from the feminist blog finallyfeminism101.workpress.com and is typical of that used in modern feminism:
Sexism is both discrimination based on gender and the attitudes, stereotypes, and the cultural elements that promote this discrimination. Given the historical and continued imbalance of power, where men as a class are privileged over women as a class (see male privilege), an important, but often overlooked, part of the term is that sexism is prejudice plus power. Thus feminists reject the notion that women can be sexist towards men because women lack the institutional power that men have.
In contrast dictionary.com defines sexism as:
sex·ism [sek-siz-uhm] noun 1. attitudes or behavior based on traditional stereotypes of sexual roles. 2. discrimination or devaluation based on a person's sex, as in restricted job opportunities; especially, such discrimination directed against women.
The definition of sexism used by feminists is itself inherently sexist by drawing a distinction on the basis of gender. The dictionary definition presented here is still not gender neutral but it should be clear that it at least accepts the possibility that women can be sexist.
Reverse sexism is a meaningless term. Sexism is sexism regardless of who it is directed at.