If they're small and harmless, then I usually just keep them out of my way.
If they're a fly or a cockroach, they have to die...
I would have a rhino beetle as a pet, though. Those things are chill with me.
The idea of an Animal Crossing mobile game worries me, especially what kind of game it will become. I just hope it doesn't end up being a "build-a-city" type of game like Farmville or Dragon City that decays after a while. The whole idea of it seems too probable.