Fascinating discussion.
I do agree with those who don’t see much difference between the exclusionary nature of athletic teams, orchestra, etc. and that of fraternities. They are all exclusionary on the basis of skills; skills that aren’t necessarily within your control to develop. Athletes are usually inherently athletic and also large for many sports. And even today, they are selective by gender. My son played his sports since the age of five, but isn’t big enough or talented enough to continue it in college. Orchestra/chorus/drama all require talent in the arts.
Fraternities are looking for well developed social skills - - and to some extent those can probably be developed more readily than the skills required for athletic teams or the arts, but it does come more easily to some. I think social skills can be considered as legitimate a special skill or natural born talent as any of the others.
In addition, at least for sports teams, there can be exclusion that goes beyond athletic talents . . .coaches look for “make up” of the kids as well. So a talented athlete, possibly more talented than others, may be excluded simply because the coach doesn’t like something about his or her attitude. It’s just as arbitrary.