Is this not supposed to be possible? I was thinking I could also change the background graphics for my island when I purchase the Hawaii Battle Theme item. It's also implied as you have to purchase that theme from the player's island store page.

Would be nice if you could change your theme :)

The Hawaiian island is sold seperately...

I was thinking I could also change the background graphics for my island when I purchase the Hawaii Battle Theme item.

i was thinking the same...
let's see in future :)