My parents were fine with my joining a sorority, just as they've always been fine with anything else I've ever wanted to do. They always said they taught my sister and me to know our own minds then just sat back and hoped they'd done a good job

I hope to use this same approach with my daughters, but somehow I think that I'm waaaaaay too "Type A" to do that!
As for initiation fees, dues, etc....it never occured to me to ask my parents to pay for those things. At that age I was very into being an
Independant 80's Woman 
My sister, on the other hand, frequented the Bank of Mom and Dad for her fees, dues, formal dresses, etc. and I guess they figured since they were footing most of the bill to send her to an Ivy some sorority stuff was just a drop in the bucket. She always was so spoiled!