Equality doesn't mean that we should all act like each other, look like each other and all be interested in the same things. Equality means for each to act the way they want without any blame for it.
Equality means for each to dress the way they want, whether you wanna dress manly with suits, casual with jeans, or girly with dresses and heals, while no one has the ability to judge you, hell while no one has the ability to judge whether you're clothed or not. Equality means you can act guy-ish or girly, you can cry, you can like cars and sports or dolls and shopping, and wouldn't be judged as gay or as a tomboy because of it. Equality means being gay isn't a shame, it means for everyone to apply their gender regardless of their sex, and only be punished for rape or pedophilia.
Equality means you can shout out that you've been raped and touched without your permission and not be blamed for it, whether you're a male or a female, no one can say she asked for it, or men don't get raped so this guy is a pussy.
Equality means when you do work, you get paid for it, regardless your sex, color or religion. It means all the rules apply to you, so you can't get away with anything because of any of the above reasons.
Equality means you can follow which-ever religion you want, and apply all it's teaching on yourself, without applying it's teachings on other people. Wanna wear a veil, cool. Wanna worship cows and worms as ancestors, fine. Wanna worship nothing and be your own spiritual adviser, brilliant. Do whatever you want, without striving to make people believe as yourself.
Equality means each person could live the life they want without being criticized for it, the only rules here is that you don't hurt someone consciously.