If “I follow the Lamb, not the Donkey or the Elephant” means I follow the Kingdom of Jesus and will live, advocate, and vote according to those values, and I will stand up to the Donkey and the Elephant when they aren’t, then I’m all for it.
But where I’ve most often heard “I follow the Lamb, not the Donkey or the Elephant” used is by Christians who also say things like “Just preach Jesus (and don’t talk about issues of oppression and injustice, despite what the Bible clearly commands).”