I think there are two different arguments going on here.
The first question, should a private club be allowed to restrict its membership? Of course the answer to that is yes. It's private. So long as it is funded and operated by the personal memberships of those involved and no public funds support it, it's nobody's business.
The second question, ought, in this day and age, there be golf clubs that that bar women members? Brown Coast's argument seems to be that it is a backward and outdated way of thinking. I tend to agree, particularly with golf on the decline as is often discussed here.
All that said, if you don't want me, if my money isn't good enough for you, then I damn sure don't want you either. Somebody else can have my time, money and business, and you can sod off.