This is too easy of an answer for a difficult topic. I know some women (and men!) who don't want their significant others anywhere near their former lovers, and I also know other women (and men) who regularly hang out as a couple with their former lovers-turned-friends. Sound strange? It can be to anyone who doesn't feel that comfort level.
It's About Past Issues
I don't think this is so much about the healthiness of the current relationship as more about the past experiences and issues of each individual person. You bring into every relationship you have your experiences, your past history, your past relationship and the attachments and connections that you've always felt.
You can have one person (woman or man) who has been consistently cheated on with former lovers, who would never be comfortable if her significant other was still involved with an ex...you can also have another person who has never had a problem with exes, is friends with their own and sees no issues if their lover is friends with their ex. And everything in between...so how do you do decide what's right, what's appropriate?
It's About Degrees of Seriousness
I do think that some of it depends on the seriousness of your relationship, how much you are willing to consider your partner's feelings and how much you are willing to compromise..how much a part of your life you are willing to share with that person.
It's About the Present
I think for a lot of people, the uncertainty and discomfort comes from knowing that the person you love and are with has a relationship with another person, once intimate, that you are not a part of. The "other" person, the ex, becomes someone to be afraid of, because they aren't a part of your current life. Therefore, it makes sense to make them a part of your current life.
My Boyfriend's Ex
You have to be willing to respect your partner's fears and feelings, and work for a compromise. My boyfriend and I have found such a compromise...we currently live together...He is still good friends with his ex. I was extremely uncomfortable with this at first. She was a part of his past, I felt, and didn't belong in OUR future..I felt she was taking away from me.
He and I talked about the situation, and found a compromise -- we found a way to make her a part of OUR life, not the other way around. His ex-girlfriend and I have met, on numerous occasions, in an effort to be comfortable with each other, we have done our part to make the mystery not so mysterious. There is always going to be an element of awkwardness, I believe...because she shares a part of him that I am not a part of and never truly will be...they will always have those memories together.
My Comfort Level
But he has worked with me to make her in the present a part of our life, and not kept their friendship separate. A lot of it is honesty, making sure I know and understand their relationship, know and understand her...and it does a lot for my comfort level. Do I want her picture up in my house? No...but I don't mind when they talk on the phone now.
Share the Whole Package
If you are trying to keep your former lovers/opposite sex friends separate from your partner, then yes, they are going to have problems. They will be the outsider, and that should never happen in a relationship. Friendships should always be maintained and respected...but I am a firm believer that once you make a committment to someone, your life should be shared as a couple..you almost come as a "package" deal...and just as you would introduce your new love to your best friend and family, you should also introduce them to those that you are still friends with.
Include Your Beloved
Make your life with your partner the most important, and by that, I mean include them in your relationships and in your friendships...you may find that the answer to your question is a lot easier then.