I'm not an American and so I have no sense of college frats. I'm thinking of Fraternal Orders which are very explicitly male-only organisations. The word fraternity literally means "brotherhood".
The choice of the word "fraternity" by the poster above was deliberate and seems to be being used to imply a more severe exclusion of others.
I've understood it the same way. We have fraternities and sororities. A gender-neutral term would be a social club.
However, I've just looked it up in Merriam Webster, and it looks like this term can include female members, too, even thought the word and the related adjective have strong masculine associations. Wikipedia basically says the same, "Although membership in fraternities was and mostly still is limited to men, ever since the development of orders of Catholic sisters and nuns in the Middle Ages and henceforth, this is not always the case. There are mixed male and female orders, as well as wholly female religious orders and societies, some of which are known as sororities in North America."
okay, then you’re thinking of Fraternal Orders, which is also something different. I’m aware of what “fraternity” means etymologically, but I’m sure you’re aware that etymology is separate from meaning.
We don't even have to argue anyway. From a dictionary:
> [treated as singular or plural] a group of people sharing a common profession or interests: e.g. “members of the hunting fraternity”.