America should care about politician's affairs because they are the ones running the country. If we cannot trust them as people, we should not be able to trust them as a politician making decisions for our country. If the politician in question cannot stay loyal to their own spouse/significant other, then why should we be able to trust them with everyone and everything? The kind of person that someone is can be revealed through his or her private life. Anyone can be put into the spotlight and turned into a completely different person, but it is how he or she acts when they are alone with their spouse that really gives perspective on that person's morals and trustworthiness.
It's been said that "inquiring minds want to know," and nowhere is this more true than in the political arena. Voters are curious about the private lives of politicians, and with good reason. It directly affects their choice of who to vote for in terms of whether or not a politician subscribes to "traditional family values."
The behavior of politicians reflects their moral code and judgement. This should include how they conduct their financial affairs as well as their marital affairs. Infidelity may be a personal topic within a marriage but it also shows the true character of a person. Politicians are not able to hide anything from the public view.
The American people do not care about politician's affairs. We have far too many more important topics to be concerned with. However, many Americans do care how politicians have treated others. Both Clinton and Trump are guilty of attacking women; making horrible comments about women they were at odds with.