Theaters of course have that right. It really doesn't matter however whether you support it or not. In the end, it's the bottom line.
To use an example that would be easily visible, let's take Wal-Mart. Wal-Mart, like the theater, has the same right to mandate a coat and tie. However, it would hurt Wal-Mart's bottom line, so Wal-Mart will never require it.
The question is: How badly would it hurt the theater's bottom line?
Sigh, I know.
It has been going on as a steady decline for years. Theaters cut corners with stage hands, and if they can park more buts in the seats by having the audience spend their money on tickets instead of fancy gowns and tuxedos they will welcome the green.
sigh.