My understanding is that the nudity ban in San Francisco came about because there was one small park which was taken over by (male, need one say) exhibitionists, with "penis rings" in place to simulate or create erections (are we NSFW yet?) It seems strange that whatever laws they have against sexual activity in public weren't enough to stop this, but this ban was the result.
Meanwhile, Steve Gough "The Naked Rambler" is on his way south through England. Visiting your neighbourhood soon!
"Apparently being naked is not considered to be a protected form of speech, unless you are a stripper."
-- I think that is a bit of a misunderstanding of the law and of the article. What is in fact said is that nudity doesn't come under freedom of expression except when it is being used as a form of expression. It doesn't say that only stripping does that -- though it does refer to a judicial decision where stripping was held to be a form of expression (i.e. one of numberless other such forms of expression-via-nudity). The decision to classify stripping as expression does seem distasteful, and reactionary in its effects, but it has nothing to do with the situation in SF, which remains liberal, despite a tightening up of the law which was a response to people exploiting the city's liberalism to go over the top a bit in ways that were intimidating to residents.
Under the US constitution speech is protected. Speech doesn't mean talking, it means expression. So generally speaking art is protected, as well as books, TV and speaking out loud.
There are exceptions for incitement to criminal action, obscenity (defined using the Miller test IIRC) and some aspects of advertising. Even protected speech can be regulated though. And it's a messy area that is subject to Supreme Court interpretations - which are cultural judgements.
If nudity is supposed to be an art (as strippers claim), or a political statement and is not obscene, then it would be protected. If it's just supposed to be comfortable, or a clothing preference, then it isn't.
In SF what they've banned will also be largely about titillating male interest. One of the issues the law in SF is trying to address is nudity in public parks that are basically gay pick up places. I think it's a bit of a shame SF is cracking down on nudity, but there have been problems with people using it to intimidate others, which needs dealing with. I think it's mainly about trying to gentrify the city though, which kills its spirit a bit to me.