that is up to you my friend. different foods give different gut floras that give dogs different mutations
you should try giving them different foods. after a dog mutates and a flora played a role you should see what the flora does in the gut flora field guide
if you want to have weird wobbledogs click crossbreed as much as you can and try to get to the lowest stability possible (the lower the stability the higher the chance of mutations (different colors, patterns, tails, wings etc))
you can have it turned off, but it will remove some parts of the game (ghosts and such)