Sharing information about someone
out of context is still a great threat. Heck, it happens all the time: a politician digs up a school paper written by an opponent who was a fiery socialist 30 years ago, and tries to paint them with that brush. And it works. So, even with the sex thing, you might not be embarrassed, but the information can and will be presented in a way to maximize your pain. You might not care about people knowing you ate a bunch of dicks, but your opponent is going to cast it, for example, as non-consensual, or will dig up some dirt on the sex partners. Perhaps they are under-age, non-consenting, or willing (with a little inducement) to simply lie about what you did.
Bottom line: information is power, and even lack of shame cannot protect you from the damage it can do in malicious hands.
(BTW your point is well taken. There was an episode of Sherlock where a (presumably young and attractive) female member of the British royal family engaged a prostitute for some lesbian S&M play - and a the gov went to a great deal of expense to cover it up. My thought was, "why bother?" People's imaginations being what they are, the biggest impact would be a small uptick in UK births in 9-10 months.)