I'm not sure if there really is an objection to populism. I suspect if you ask 100 different people to tell you what is a populist, their answers will probably be all over the map. I also suspect that if you read the definition of the word (populist) out of a dictionary, most people would probably discover that they too are populist. They just didn't know the actual dictionary definition.
I found a dictionary definition of (populist) from three different dictionaries
First dictionary: Populist is defined as a member or adherent of a political party seeking to represent the interests of ordinary people.
Second dictionary: Populist is defined as a member of a political party claiming to represent the common people.
Third dictionary: Populist is defined as a supporter of the rights and power of the people.
Based on those dictionary definitions I suspect that virtually everyone would see themselves as a populist. They probably don't really know the dictionary definition of the word.