" How do I deal with this issue?"
How you manage this would depend on things such as 1) what is the one part of this that makes you most uncomfortable (self esteem, trust issues, feeling disrespected, etc) 2) what outcome you're seeking (allowing yourself to be flexible, remaining firm that it is something you are not willing to entertain)
Another issue may be whether or not you are still hesitant to enter into a relationship because of fear of disappointment/heartache.
If you want this to be an experiment in the beginning and see how the two of you get along, how the relationship progresses, what sense of autonomy each of you still maintain and how close emotionally you get with one another, you can give it a chance.
All new relationships hold a risk and only by taking a chance would you know what the possible outcome can be. She could have kept these "friendships" on the side without informing you of her intent. At least she's been honest from the start. You can try to determine what is her own motivation behind it. Most importantly though, is in determining what exactly is causing you this internal struggle and address it. That would be the first step in how to deal with the issue most affectively. If your beliefs and expectations don't match hers, think about whether or not you want to pursue the relationship and why or why not. At no point should you make yourself do or agree to something that is in conflict with your beliefs and desires.