That second sentence may be true under some strained and highly unusual definition of "public" - but that definition clearly has no legitimate bearing on privacy rights.
There is no legal right to privacy. The Supreme Court in Roe vs. Wade invented what it said was one in the Constitution—but it couldn't find the word "privacy" in the USC. So it identified what it called a "penumbra" (shadow) of a right to privacy—which it then claimed made laws against abortion unconstitutional. This decision was nonsensical, and itself unconstitutional on a number of grounds.
Privacy is real and important, even a sacred thing. But it is a general effect of our explicit rights—freedom of speech, association, due process, search and seizure, etc. And legitimately, it will always be a matter of degree. Because we live together, we have some legitimate concern about the effect of other people's actions, even if the effect on us is indirect. Such as drug-dealing, to use an example from trade. To a (much) smaller degree, our legitimate concern also applies to trade in things that are legal: People in business selling stuff legally to strangers on the street or behind storefronts have a more reasonable expectation of scrutiny or curiosity than folks regularly employed at the same company, sitting in an office, working together all day.
The same prudential idea of privacy applies to social relationships involving marriage and sexual behavior—which have much more impact, positive or negative, on the surrounding society.
How does unmarried sex behind closed doors "impact" "society" any more than married sex or unmarried Parcheesi?
And, to return to the original topic, how do certain unmarried sex acts "impact" "society" more than others?