Thanks for your openness and candor. Like yourself, I was raised in the church and became very familiar with the Bible and Christian teachings, etc. One thing I realized is that I needed to be able to stand alone on my faith, not just accept what I was raised to believe. In my 20's I had my own crisis of faith, and fortunately God was able to reveal Himself to me and show me who He really is. That kind of personal understanding and faith is something all the years of sunday school could never give.
And you are right, Jesus was so open in His associating with sinners, (prostitutes), thieves and the "losers" of society that He was routinely criticized by the religious teachers of the day. Jesus' response was formed in such a way that it defined His relationship with these "sinners" when he said in response to the criticism, "It is not the healthy who need a doctor, but the sick", obviously identifying the people's need for salvation and His ability to provide it.
Now what your girlfriend is saying is coming from the Apostle Paul, when he warned Christians in the early church not to associate with people not of the Christian faith. Paul went on to state in other places that he was not advocating a retreat from the world and for all Christians to join a monastery; that is not a correct interpretation of the passage. But Paul did make it clear that the type of associations he was referring to were those relationships that are interpersonal, where we rely on others and they rely on us, including emotional bonds.
The principle makes sense if you think about it: As Christians, we claim to be committed to Christ and His teachings, and when any relationship stands in opposition to those teachings or calls on us to do things we cannot do in faith, we are to always choose to be obedient to Christ. That principle will, without exception, cause conflict and tension in our relationships. But we must follow Christ above everything else.
Relationships, especially romantic ones, are the most prone to disruption by a believer in Christ and a non-believer being together, because a romantic relationship involves opening ourselves up to the other person and being emotionally vulnerable. A verse in Proverbs states: "Above all else, guard your heart, for it is the wellspring of life". Even two Christians in a relationship are prone to tension, so for two people who hold opposite views on the most important question of life are doomed to suffer.
I know this is not what you wanted to hear and it is true that being a Christian requires us to love even our enemies, but in life we are always forced to choose who we ally ourselves with: People, materialism, money, values, etc. And by choosing one set of values over another, we are saying yes to one thing and no to another. If you say you are exclusive in your relationship with your girlfriend, you are by default saying "no" to all other girls. By a Christian saying they belong to Christ implies that they are in a process of brining everything else in their life under His authority. And if He tells us not to do something, then we obey (or try to obey, although imperfectly), trusting in faith that He is doing so for our own good.
Just some thoughts, and I hope this helps clarify your dilemma. And as a person who was raised in the church, walked away from His faith, and was eventually came back to God by His kindness and mercy, I would encourage you to examine the true person and work of Christ. I guarantee you that you will meet a person you never knew.