How secure is this supplier in their relationship with your company? How much influence do you, personally, have over decisions to award them contracts?
I work in a client-facing professional services job so we are the “supplier”. It would be a massive mistake for us to organise an event and deliberately exclude one person while inviting their peers. We might organise something that potentially only has niche appeal (a recent example is a marquee at a Rugby event) but we’d invite everyone and let them decide if it was for them or not, and we’d balance it with other events with wider/different appeal.
With golf, some of my colleagues do play with individuals at some clients, and those games tend to be organised because they have similar skill/experience, and are probably members of the same club anyway. But that’s no different to me taking a few individuals out to lunch or to a show.
What really stinks here is the assumption that as a woman you would not be interested in golf. I also have the sense that novice golfers not welcome at the event? My mother in law is a very keen golfer and her club is stuffed full of ladies. My husband, a white middle class man who works in banking, has never picked up a golf club in his life! Tell me, is every other man in your organisation a competent golfer? As others said, there are so many social reasons why it’s not a universal male hobby either.
In your position I would not be letting this slide and would be having a serious conversation with the supplier about what a massive insult this is to you. It might get them to up their game generally as they grovel not to lose the business, even if there is no real risk of that. Win win, right? You have power here, use it.