With the recent events in mind

As a Caucasian woman, I always feel like if I speak about racism, I am stepping over a line. As a privileged white person, I have never had to experience things that racial minorities have had to face. But I also feel like by being silent, I'm allowing things to happen. I grew up in a home where my father was extremely racist and in high school, I dated black men so I heard it from my family that colors shouldn't mix. My grandfather on my dad's side was a klan leader. I just don't even know if I have a right to say anything when my family history is full of hate. I guess my question is, as a white person, how can I help to end racial injustice?