I am unsure if this is a bug or the Internet being dumb, but just in case: I set my phone down for a moment, and the screen turned off, so when I unlocked it, I had to restore the game. I could hear the "bloop" noise for pressing on the little animals, but I couldn't move anything. Then I noticed the fox in the corner was greyed out and looked in transition, so I couldn't move anyone else or the fox. Nothing else to do but fully back out, then restart.
I tried going to different tabs and locking my phone again to induce a restore to see if it would fix it, but it was always the same thing.