Getting BACK to the issue at hand,
If you claim to be a Christian while dating this guy who called himself Catholic but didn't live his live that in any way represented Christ's way of living than you are just as much a 'heathen' as he is for still dating such a guy.
You CANNOT evangelize a person while dating them, because you end up sending all the wrong messages. You're teaching them that you can do your own thing while still wearing the 'Christian' badge. You are teaching him that He is God NOT Jesus, you are teaching him that your life revolves around him and not Jesus.
Obviously his Catholicism was a mask. Just like their are fake Calvinists, Methodists, Evangelicals - it doesn't matter, he was a fake. His unchristian living should have been the first red light for you to run for the hills and never have anything to do with him. But you say you love him, enough for you to ignore those red lights and enough for you to be confused about where you stand on him converting to Islam! I suspect this is because you have or still are in a sexual relationship with him. Stubbornly remaining in obvious sin usually has sexual roots somewhere, I know because I fell in this very same trap myself once upon a time..
You need to seriously, (on your own) come before the Lord and ask him to show you your sin, it will grieve you but it will be for your benefit, and you need to come to a repentance of the heart. And the heart of the issue is this - idolatry.
Secondly, once you've done that you need to break up with this boy!! PERIOD!! You may have thoughts like - 'But hes the best I'll ever have.' That is a lie from the Enemy. 'He loves me.' He may have a visage of 'love' for you, but it is not the love God wants you to recieve. God wants you to experience his Holy love as well as the Christ centred love from another godly man who will love you like Christ loved the church. You are missing out on that and you don't even know it! God wants you to experience the practical love where a man lovingly leads you, prays with and for you, raises his children according to the bible, God wants you to experience the joy of marital intimacy not sexual immorality that the Enemy has convinced you is ok.
Lastly, you need to be in a close knit community of strong godly Christians. If you think you belong to a church now, you're wrong, maybe you go to church on Sundays and do nothing else. Thats the problem, when you're involved with your church community you come under that warm loving guidance and leadership that transfers into your own life. As a person previously tied into sexual sin, its hard to go to church and be in christian fellowship every week because the Holy Spirit is nearby and you always feel convicted of your sin which you don't like because its reminding you that you are wrong and what you are doing is wrong. Thats why people who are in really heavy sin, stop going to church.
And if you remain with this boy you are turning your back on Jesus and are following the Enemy. Not saying that Islam is Satans primary tool, many other religions and whatnot are as well. Reread Genesis, Satan attacked and manipulated Eve first because he knew of the influence she had over Adam. Secondly, whether feminists beleive or not - we as individuals, families, communities and countries follow our men. And it starts in the home. If you stay with this man you will invariably convert to his ways, and you will either go willingly and completely forsake your Lord as God or you will go grudgingly and will remain miserable because your differences in faith will always rock the boat, and if God forbid you marry and have children with this boy then they will follow him not you and they will not learn and come to know Jesus as they ought.
Do the right thing.
I recommend you watch these two videos, it is sermon content from a godly pastor that my husband and I listen to:
http://marshill.com/media/religionsaves/sexual-sin
http://marshill.com/media/religionsaves/dating