The LGBTQ rights movement shows us the same thing. Look at how politicians who used to advocate discrimination modified their stance when family members came out to them. It didn't stop institutions from discriminating against LGTBQ rights directly, but enough brothers, mothers, sisters, sons, best friends, etc. coming out on a one-on-one basis eventually took the wind out of some of the institutional discrimination.
The idea that a group of people are less than human because of a particular characteristic is what enables this kind of institutionalized hatred. However, if we open enough one-on-one respectful dialogs across the lines that propose to divide us, the institutions that support those divisions will lose their support and melt away.
There is a long way to go. Racism, sexism, homophobia, etc. are rampant not just in the western world, but globally, and institutions reinforce these boundaries daily. However, with enough mature dialog by individuals, we can wear down hatred with respect.