Before I get too far, I should offer a definition of "sexism," because I use both this term and "reverse sexism" in situations where one sex is being favored over the other.
What I mean by "sexism" is "an institutionalized system of privileges and rights granted preferentially based on sex." Whatever is more prevalent in an institutionalized system is termed "sexist," and reactions to that are "reverse sexism." So, because "sexism" is traditionally discriminatory towards women, I use "sexism" to mean "favoring men" and "reverse sexism" to mean "favoring women." Hopefully soon I won't be able to distinguish whether I should be using "sexism" to mean "favoring men" or "favoring women." (In some places, such as the family court, it is already more appropriate to use "sexism" to mean "favoring women," but until we get rid of a few gender stereotypes, I won't apply the terms in that reversed form universally.)