Normal that someone you encounter in your everyday life is gay and it's totally not relevant to the encounter whatsoever.

Normal in this context means that the person's sexuality isn't important.

This is why we're seeing such a huge pushback from the political right wing across the world against the LGBTQIA community. They know they're losing. We're normalizing it and it terrifies them.

This. It's so important to change the narrative. They're acting like it's normal because it is.