Perhaps the word "protections" would be more accurate. For instance, protection from discrimination in the work place. Also, there are some rights that are unique.
Women are able to get pregnant. Men cannot. That is not about rights, that is biology. But stemming from that biological fact, is the question about whether women have the right to get an abortion. Obviously, men don't have, want, or need the right to an abortion, because they don't have the ability to get pregnant.
Also, same sex marriage is a gay rights issue. However, if we erase gender from the equation, it is simply about the right of two people who want to get married, to get married. This is not necessarily a gay right. Straight people are allowed to have same sex marriages, but they lack the desire to do so.