I suppose if you had an airline called "cleavage air" and had all the flight attendants wear low-cut tops, then you might get away with it.
The only way Hooters could in principle discriminate on the basis of race is if they come up with some first amendment pretext for it; e.g. the waitress job is actually an artistic performance and for some reason the art demands the performer be a certain race. That works for movie productions, but for a bar hiring waitresses? In practice it wouldn't work because the courts and the public would both write you off as an obvious racist.
I'd be interested in something that gives more context, details and examples than the wikipedia article, but not targeted at lawyers and not excessively long.
How does that work in practice for a company like Hooters - do they spend millions on lawyers to be able to defend their position? What if you'd open a local place working in similar way to Hooters - would you go bankrupt trying to defend yourself?
They certainly spend millions on lawyers. They've been sued for not hiring men several times, AFAIK always settle out of court. They defend their position by claiming being a woman is a BFOQ for working at Hooters, but aren't eager to risk losing in court.
It doesn't take a lawyer to tell that Hooters' primary product isn't chicken wings (Chris Rock even made a joke about it).
The reason behind the laws isn't common-sense, in the case that the 1964 Civil Rights Act is basically a list of "things currently happening that we think are bad" rather than an exhaustive list of things it's bad to discriminate on; it's also limited somewhat by the legal framework that the US congress was working within.
Labour laws in the US are also weird for similar reasons. There was a point at which union members were beaten and killed, with the local police being bought-off to not intervene. It escalated to at least one pitched battle between a private army and workers. Things like assault, battery, and murder are enforced at the local ("state" in the US terminology, not in the meaning everywhere else in the world) level not federal level, so rather than arresting the people doing this, laws were passed giving special protections to unions. Then a few decades later people argued that the special protections made unions too powerful and a bunch of extra rules limiting what unions can do were passed.
