It seems like two politicians can do the same thing, but the resulting scandals are very different. I have a pet theory of why that is, consisting of three separate parts.
Expected moral high ground. If a politician avoids paying taxes or is otherwise tricking some authority, it will rightly and likely result in a scandal. How bad the scandal becomes, frequently seems to depend on where in the political spectrum they exist. From a politician who claims to believe that taxes and welfare are good for society, the dissonance between their actions and their words becomes larger, resulting in a more potent scandal. Similarly, I would expect a socially conservative politician having an abortion, to affect them more than if their socially liberal counterpart did the same.
Acceptance or denial. In normal social life, there are norms for when you are allowed to deny responsibility. When reality is denied in the context of romantic relationships, it's called gaslighting. It seems like some politicians can forcefully deny reality, and people around them don't know how to react. The result is that the denial of there even existing a scandal causes it to disappear.
Gender and race. Scandals seem to affect women and minorities more than their actions alone would suggest.