Equivolent of 'But Not Too Black' when applied to cartoon animals. Everyone likes a quite little woodland critter - until they have the nerve to start acting like an actual woodland critter. Or fan art depicts them as doing so. Flavour of the month would be the kind of reaction you get from MLP fans when their favorite character is given 'undesired' feral (animal) traits. Like appearance or behaviour or social outlook.
Compare with 'But Not Too Black' and 'But Not Too Foreign'. Contrast with 'Funny Animal Anatomy', which is imposed externally artistic decision - not a negative reaction of the audience to the unfamiliar.