There is a difference between making fun of someone for personal characteristics and for their political beliefs. However, the specific word “bully” or “bullying”, and all the baggage that comes with it, is a pretty loaded word with an almost exclusively negative history and connotation behind it. One that’s had a real negative impact on many lives, the vast, vast majority of them undeserving.
I think there’s better ways to keep making fun of chuds/libs without adding to an already existing culture of bullying.
Using the word "bullying" positively is cringe.