To fight for equality is the moral thing to do. And by equality I mean the right of any person regardless of gender, age, sex, and religion to enjoy rights that everyone else is enjoying.
How moral is it really to enjoy certain kinds of liberties if others are not enjoying these liberties as well?
Kindness. Compassion. Empathy. Morality must be grounded on these virtues. How can one be human if we are preventing others from being human?