When does an Ex stop being an Ex and become your friend, and is it fair to make your partner deal with it?

I'm trying a slightly different tactic here, and opening up the floor for discussion on what I feel might be a controversial topic.

There's a girl at work who's getting married in September and she maintains a close friendship with her Ex-fiancee (now thats a whole different story...). Now her current fiancee isn't terribly happy with this arrangement and I feel this is totally justified. She has told him that if he forces her to choose between the two of them that the ex will win and he'll lose her.
Now I would have thought that the man you were marrying was a little more important than the the ex? Or is that just me? I'd like some active discussion here people. I think she's being unfair, but at the same time, should we have to choose between friends and boyfriends? I will also allow here that the friendship you have with Jimmy Joe from high school that your partner "doesn't approve of (maybe because they make you do stupid things etc)", is entirely different to friendship with Exey. From my perspective she should be taking his feelings into account and distancing herself from this damaging friendship.
I would hope in this position that I could take my partners feelings into account and that he would also take into account my desire for the friendship to continue and we could come out in a balance for the two of us. Is that possible? Who wants to take up the baton?