This style of comedy is popular due to how well it is received by the majority of the population. About 2/3s of the population votes while 1/3, mostly centrists, choose not to. Regardless of which party is being targeted with a joke, at least roughly 2/3s of the audience will find it funny. Comedians often bounce between which parties they target throughout a performance which helps keep that kind of shame balanced.
As a person who finds this type of comedy funny. I love it and recommended it to anyone.
I agree with Fisher! The jokes are funny for both sides, that is why this style works so well.
I think the ability to appeal to at least 2/3 of people will tend to help the popularity of this type of comedy. But I believe this type of comedy makes hearing bad things about topics you agree with easier to understand.