People who "call themselves" Christians aren't necessarily Christian. So some will be rescued (raptured) and some won't. Likewise, some people who do NOT call themselves Christians actually will be rescued.
What matters to God is whether or not you believe him. He won't force you to believe him, because that would make him a big joke, a big puppeteer putting us all on strings.
The agreement God has made, with every person who ever lived, is that he will treat you like a perfect father would, if you let him. God wants to be closer to you, always. But you must trust him first.
Most of all, he made a great sacrifice, and suffered and died in your place, for anything bad you ever did or ever will do. Your right to live with God is given if you simply believe that. Everything you do after that just determines how he rewards you. Many churches get this wrong -- "salvation" is given just for believing, "rewards" are given for good works.
There are so many proofs of God's caring for us in human history, but since you mentioned "rapture" in your question, here is a little about the future.
God knows human nature, and he knows what the world is becoming. At some time, probably soon, world leaders who don't believe God will bring the human race to the edge of extinction. This will be in the final few years and months before Messiah (Jesus) returns to Earth. People who DO believe God, before it begins, will be rescued from those horrors.
Some people won't be rescued, because they didn't believe God before the madness started. But even for them, it won't be too late to start believing. They will suffer more than any generation of humans in the history of time, but God will still hear them if they trust him.
But then some people will die, before or after the madness begins, who still refused to believe God. I wish I could say they get another chance, but the Bible doesn't tell us that. For them, we don't know exactly what God will do, but they certainly risk being separated from him forever.