Just wanted to let all those who are curious about an IUD and your cup...it is A-OK! I just got my GyneFix inserted today and made sure to ask that question. I am a brand new Diva Cup user but due to the increased bleeding i'm about to experience I wanted to get away from changing a tampon every hour...because where I work that would just be awkward.
Dr. Hall at the Willow Clinic did the insertion, and she told me that I would be totally fine using a Diva Cup with my brand new IUD, but to hold off for the first month due to the risk of infection. So I will stick to my cloth pads until that time. She kept my strings long because she said it was easier to push out of the way and would be more comfortable for my partner. In 6 weeks I go back for a check-up and if i'm not happy with long strings she will trim them super short. I was worried about grabbing the strings with my cup but she told me that I won't be able to pull out my IUD that way. Woo happy day!