(Denny Crane: "Sometimes you can only look for answers from God and failing that... and Fox News".)
Well, I have only been to a strip club once for a bachelor party but that show certainly said something to me!
This is not a First Ammendment issue. It's a Fifth Ammendment issue. The reason is because it's the Fifth Ammendment that recognizes the Right to Liberty--and the Right to Liberty is the reason that it's Unconstitutional to criminalize the actions that occur in these night clubs. The Right to Liberty is the right to do whatever does not violate the rights of others.
There is an expansive view of the First Amendment when it comes to unimportant things like the "self-expression" of dancers in bars but, as you noted, the First Amendment is not seen protect anything important like political speech. Speaking out about an issue or a candidate before an election is an intolerable act of corruption (how dare mere citizens take politics into there own hands), but some nekkid dancer's self-expression is a precious First Amendment right.
That, and the First Amendment is seen as only protecting the counter culture. If an artist uses public funds to make "art" featuring, say, a cross inside a toilet and this "art" is displayed in a public museum, well, this "art" is a precious expression of First Amendment rights that we all must fund through taxes. But let there be, oh, I don't know -- a privately-funded cross on public land in San Diego commemorating war hereos, and suddenly a cross becomes an intolerable violation of the First Amendment.
Well, that is a part of it... The main reason is that the ban on stripping was a direct violation of the MO State Constitution. It's got a feature that would be WONDERFUL in the US Consitution: There's a provision that you can't just tack-on amendments to a bill that have nothing to do with the original bill's intent. Can you imagine how a ban on that sort of nonsense would cut back on pork spending, as well as "little surprises" when legislation passed? Heck, some legislators might actually try reading the bills before they vote on them! And there would be no more 900 page omnibus bills!
What happend is the guy behind the bill couldn't get enough support for the bill to pass on its own, so he tacked the provisions on to (I believe) a bill that deals with drunk driving (I can't remember the exact bill right now). That's what violated the MO Constitution.
Mark