Perhaps sex with a Trek equivalent to Cthulu perhaps? :P
I'm not sure. It really depends on how prudish humans in the 24th century really are. What would make them so disgusted that impeachment was necessary? Or do they simple figure that is a personal thing and what matters is the person's ability to lead the Federation or represent their world on the council or whatever? Anything else is just a private matter between the politician and their partner.
Weren't there a group of prudish people in that oft-hated DS9 episode "Let He Who Is Without Sin..."? Maybe they would be bothered if a future presidential candidate was not married or if they cheated on their spouse.