As much as I might PERSONALLY disagree with it, so long as you don't cross certain lines, you have a right to be as sexist as you want.
If Augusta was receiving federal funds for something, or tax breaks, or if public business was being conducted there, you might have an argument to force them to open their membership. But what's private is PRIVATE and they have that right.
...just as I have the First Ammendment right to state my opinion that their policy is Neanderthal-like.