The average American spends too much time at work to not have some sort of social, not 100% related to work, activities and groups that they can be apart of. As a black employee I'm very plugged in the employee resource group for black employees at my organization. I've been able to give back to the local community through volunteering, develop mentee and mentor relationships through this network and develop a sense…
I wish people of my color, gender, or belief were allowed to make a club, or join yours. It sounds great. Maybe something like this is why whites commit suicide so much more than blacks in America (per CDC [1]). Blacks suffer in many ways but at least they're allowed to make a community just about themselves, and that's valuable. [1] https://www.realclearscience.com/journal_club/2013/04/05/us_... !
I work at a small company (c. 600 people), so it isn't big enough to have these kinds of groups, but I'd be more interested in joining a group based on interests, like software development (I do work for a software company), or maybe tabletop gaming. I don't care what race people are, but what their interests are like. Of course, I'm a white guy, so there wouldn't be a white guy group (nor would I want to see one).
And for what it's worth, there are a lot of immigrants at this company, so whites are a minority among mostly Indians and Chinese, etc.