In days long past, very few of the puppets in sesame street were actually all that human looking, such as oscar, elmo, cookie monster, and obviously bigbird and snuffy, with some looking quite bizarre. Among the most "human" looking were ernie and bert, who were both quite boldly yellow. Most of the puppets were arguably adults, with elmo being an obvious exception. At the same time, they were also usually complimented by a large number of real-life kids, often of varied ethnicities.
Over the years, many changes occurred, such as regulations relating to child labor, and funding challenges for PBS. As a result, they used fewer actual children. In the long run, it became more feasible to use more puppets, and less people. It cut costs and avoided legal complications.
So part of the reason it seems weird to see puppets of one ethnicity of kid or another on sesame street is cos at one time there really weren't any kid puppets of any ethnicity, or at all.
As for the republicans attacking a puppet, one can hardly be surprised. Many seem to prefer attacking things that don't actually exist in real life.