If a Muslim restaurant owner refused to seat women not wearing the hijab, the government of California would bow down and worship him. If an Orthodox Jew refused to seat women and men together, there would be a class action lawsuit and they'd drive him right out of business.
And I quote Ayn Rand in asking "Do you want to be lying on a table at the mercy of a man holding a knife, when you have compelled him against his will to operate on you?"
Frankly, my dear, I decline.
Doubtful. That's a pretty clear case of sexual discrimination by a business owner. There might even be a violation of federal law there.
The business owner could get around this by requiring head-coverings for all of his customers. You can institute a dress-code for customers, it just can't be discriminatory.
If an Orthodox Jew refused to seat women and men together, there would be a class action lawsuit and they'd drive him right out of business.
A rule like that wouldn't violate any discrimination laws, AFAIK.