Yes, normalize as in to make normal or standard behavior.
https://freerepublic.com/focus/f-news/4068894/posts
A pride-month event at a Dallas gay bar inviting children to take the stage alongside drag queens was met with outrage and encouragement alike over the weekend.
The event, titled ‘Drag The Kids To Pride,’ was held at the Mr. Misster gay nightclub in North Dallas on Saturday morning.
The event invited parents to bring their kids along for a morning drag show, and featured children dancing alongside men dressed in drag beneath a pink neon sign reading ‘It’s not gonna lick itself.’
Outraged protesters arrived to picket the event, while the shows promoters and participants defended the day as nothing more than an opportunity for people to share joy about who they are.