My parents weren't against me joining a sorority, but they were somewhat resistant to the idea at first for several reasons. One of which being the stereotypes, and another was the cost. As a junior, joining a sorority was not an expense they had planned for ahead of time.
I talked to them about it gradually and involved them in the whole process. I visited our Greek Affairs website with my mom, pointed out friends of mine who were in sororities, and gave them links to the national websites of all the sororities on my campus. And throughout rush, I would call home each night and tell my parents what I had done that day and how I was feeling. It wasn't until a few hours before Pref Night, that both of my parents told me to go for it and not to worry.
I think the logic behind it was to see how badly I really wanted it. If it was just an impulse they could talk me out of, or if it was something I was really willing to stick out. A few weeks ago, my mom told me it's the happiest and most outgoing she's ever seen me and that they definitely made the right choice in letting me join.
Long story short, it's definitely possible to win over parents who aren't exactly thrilled at first, just try to keep them as informed as possible. Good luck!