If this in the US, private clubs like golf clubs are allowed to have membership policies & rules that discriminate against certain members based on sex. So long as membership in the clubs is voluntary. As employers, clubs have to abide by federal, state and local anti-discrimination laws, but when it comes to the club membership, it's permitted to discriminate based on sex so long as that's what the club membership wants. Hence, the continued existence of all-male clubs, and of such features as "the men's grill" and "men's smoking lounge" in mixed-sex clubs.

Also, private club managers/directors don't make the rules in such clubs. Rules are made by rules committees made up of members, and agreed to by the board (of trustees, overseers, whatever the name). In some clubs, the entire membership votes on rule changes. In other clubs, it's done at the committee and board level.

Women who are members of such a club need to organize with other female members, and with male members. Especially those with clout and $$$. A factor to consider is whether the women became members of the club on their own, and pay their dues from their own funds, or they obtained membership because they are or were married to men who were the primary applicants and will be considered the real members.