I can't have live photo als a background (I can't even touch the live photo option) what can I do?

I have this

On my iPhone 6S, running iOS 9.3.2, I created a live photo in Camera Roll.

I then went to Settings > Wallpaper > Choose a New Wallpaper > Camera Roll and chose that wallpaper.

That gave me the following choices:

It's a bit hard to see at the bottom, but I am offered to use Still, Perspective, or Live Photo as the wallpaper.

If you encounter different actions or responses, please elaborate.

I had this same problem i soon found out that when you are in low power mode you cannot use/set live wallpapers. Try turning off low power mode and see if it works, if it doesnt then it must be a bug. Hope this helped