First rule of business: In God's time. We have a tendency to want a person to accept Christ right now before anything bad happens, forgetting that God is in control, and that we are but his servants. In other words, it may take years for a person to get to the point where they're fully ready to accept Christ.
Now to your question: Yes, my grandmother was a devout Muslim, and became a Christian when she dated my grandfather (an evangelical Lutheran). Mind you, this was in Indonesia in the late 1920's. Today, I still have family in Indonesia, some who are Christian, and some who are Muslim, and they certainly don't disown or ignore each other in any way.
The great thing about Christianity, is that, at its core, it's not a religion, but a relationship. I've known a few former Muslims who now attend Christian churches. I've also known a few Muslims who are Christians, who still practice Islam. I know some Jews who are Christians, who are still active in the temple they grew up in, too. One of my neighbors is a Muslim. One of the nicest, most caring and loving people you'll ever meet. We've talked about religious topics many times. His views of Christianity are very positive, mostly because, according to him, I discuss the topic in a respectful manner with him, and I respect his religion also. He recently told me that he believes it likely for Jesus to be the Messiah and Son of God. Now, at this point, I could either force the salvation topic down his throat (at the risk of pushing him away), or allow to simply share my faith with him, and allow the Holy Spirit to choose the time of his salvation. I know this might sound a little ecuminical, but God dwells in the heart, not the institutional edifices, so frankly don't worry much about that stuff.
Did that make sense, or did I lose you?