In order for any deviation from what the majority of people in this country consider normal to change course and become a part of a paradigm shift, it must be seen and understood as such first. To be considered normal, one must change that which is the "standard; usual, typical or expected."
That change is an individual one. You can't force the definition to change upon society by legislation or protest. Change doesn't come from shaming people into silence, it just makes them hide. It doesn't come from a series of Facebook posts (or blog posts...). Change doesn't happen because you vocally support a cause or align yourself with an ideology.
In order for the definition of normal to shift, we each individually have to challenge it in practice. In order to normalize things, you have to deviate from the norm and encourage others to do the same.
Women fought for and won the right to vote almost 100 years ago but still don't make as much as men do in the workforce. The Civil Rights Act got rid of Jim Crow laws 50 years ago and yet racism prevails. Being gay in America is now generally accepted and marriage is legal, but the trans community is still heavily marginalized.
Redefining normal for society requires small but significant individual acts.
Chef Coco Winbush once told me "If you want to change the world, have a meal with someone who doesn't look like you."
To adjust normal I'd suggest you have a meal (because we all gotta eat) with someone who doesn't think like you as well. Have that meal someplace you wouldn't ordinarily go. In a neighborhood you find yourself judging without on-the-ground intel. Ask questions. Get in disagreements. Drink no one's Kool-Aid. Eat some food while you do it. It's not about agreement or immediate Kumbaya understanding. It's about the act of being seen to have that meal. It's in the act of making these meals among people who cannot agree but still like to eat normal.
If that's too radical for you, fucking have a conversation with someone who doesn't think like you on a train or waiting for a bus. Share a Power Bar. I mean, baby steps, right?
If you dig the present definition of normal, look around you. It's being redefined whether you like it or not.