What would most guys do?

My girlfriend and I took a break after almost two years. During that time she made a guy friend, messed
Around with him, slept over a few times, text him all the time and lied to me about her whereabouts, actions, etc. the entire time. I know we were broken up up she knew I was bing faithful and trying to work it out. We were still seeing each other, talking and even sleeping together, just no official title of bf/gf.

Obviously her physical actions and emotional attachment to him hurts but was since in her mind single okay. The lying was not okay.

We are now back together again and working on us but trust is a big concern. She has come clean about all that has happened down to the painful little details but says they never had sex.

My question is should I be okay with the fact that she wants to keep him around as a friend or as a woman that loves a man and wants to be with him should it be clear that this will keep the wound open and is not only disrespectful but absurd. She only knew the guy a week and we have fought a lot about it. She is still Facebook friends and thinks I'm out of line to ask her to give up a friend, and severe all ties.

Am I out of line or right to protect the relationship and our future by insisting these type of relationships are not healthy?

You can't force or insist on your other half to do things, it only fuels them to do whatever it is more. It's up to you if the relationship, where it's at, is good enough for you to try and move forward. Going back is never a good idea, imo.