The Saints Row games are the only ones I can think of where streaking and exhibitionism are actually fully fleshed out mechanics that are built into the game without relying on mods. 

In Baldur's Gate 3, you can run around completely naked from the beginning to the end of the game and can customize your character's privates. There are even viable builds and strategies revolving around bonuses applied to characters not wearing clothes. The only odd thing about the nudity is that it's almost never referenced in-game, and there's in fact more dialogue in the game if you talk to certain characters in your underwear or in scandalous outfits rather than naked. 

While you can't get completely naked in the Elder Scrolls and Fallout games, in most of them, NPCs will react to you running around in your underwear. While in Skyrim, this mostly leads to amused or angry comments, in older games, you could miss out on dialogue and quests if you were naked all the time as some people would instantly hate you. In Fallout 4, some companions like Cait and Hancock will approve of your exhibitionism and gain affinity while the more prudish companions will ask if you're cold.