Short answer: yes, Saints Row IV contains nudity and sex. What is important however, is to which extent, which I will elaborate and demonstrate with images.
Therefore, if you do not wish to see in what way, shape or form sex and nudity are implemented in Saints Row IV, please take the short answer and stop scrolling.
Nudity in Saints Row IV
Nudity in Saints Row IV can already be found in the very beginning of the game. Your character will be completely naked (full body nudity). However, the important bits are censored with big blocky pixels. When you arrive on a space ship, you will be dressed into a proper suit.
Other than that, you will also find Matt Miller completely naked and vulnerable. But again, properly censored. No dangling private parts in this game.
That being said, there is actual upper body nudity in the game for whoever pays attention. The magazine Keith David is reading contains an image of Shaundi (Saints Row 2 style) on the cover, she is not wearing a top and her nipples are uncensored. This image of Shaundi can also be found elsewhere in the game, as a poster.
Sex in Saints Row IV
As for the sexual content in Saints Row IV, there are plenty of sexual references and direct communications about sex. For example, the Romance features in Saints Row IV are sexual, but no sexual acts are depicted on screen or off screen, except for one – the Romance option performed by C.I.D. briefly shows C.I.D. ‘going down’ on your character. Your character, however, is not and can not be naked. You will always wear a suit on the space ship. What is depicted on screen in some Romance cut scenes, is kissing, but only shortly.