I find it strange when I hear someone ask "can you be a Christian and...". You can be a Christian and do just about anything. The question we need to ask is, is it a Christian thing to do? You can be a Christian and sin, because otherwise you couldn't be a Christian; you're always going to be a sinner (1 John 1:8-10).
So again, the question you should be asking isn't "can you be a Christian and", but "should you be a Christian and". Note that word "should". We definitely shouldn't be testing the limits of our salvation. Think of it this way: You know those yellow lines that tell you how close you can get to a train track before it gets dangerous? Do you walk right up to them and put your feet mere millimetres away, or do you stand at a safe distance? God's anger is a little bit worse than being hit by a train...
So we can ask things like can a Christian vote Democrat, can a Christian be gay, can a Christian believe in Evolution etc., and the answer to all of those things will never be clear cut. If you confess Jesus as Lord and believe in your heart God raised Him from the dead, you will be saved. But what does it tell us if you're testing the limits of that salvation? God alone knows your heart, but what it tells the outside observer is that actually, you don't really confess Jesus as Lord. You may be expressing sorrow for sin, but it is not Godly sorrow of the kind that produces repentance, but worldly sorrow of the kind that leads to condemnation (2 Corinthians 7:10). Think of it as the difference between being sorry you committed the sin and being sorry you got caught.
Ultimately, I think we all make this mistake. How many of us have been through that thought process of "yes, this is sin, but I'll repent of it later and God will forgive me"? I'm certainly not going to pretend I'm innocent in that regard. Are you? But while this is a common temptation, it is also an unholy one. A great phrase to remember is "God prefers obedience now to repentance later". Do you know what you're doing is sin? Then stop. While we are on this earth, we're always going to struggle with sin, but let us make sure it is a struggle. We are at war with this body of death, and if we fall, we should make absolutely sure it is a fall. No soldier runs willingly into a bullet! What Christian should run willingly into sin?
It really does say a lot about the state of our faith when we ask "can I be a Christian and...". How much can we get away with and still be saved? Quite a lot, as it turns out, but if we are truly saved, how much would we really want to get away with? The person who wonders what he can get away with and keep his salvation probably never had salvation in the first place. Faith that doesn't change the heart is no faith at all. Therefore, let us ask the faithful question: What should I do as a Christian? If you ask that question in sincerity, you will stay well within the Lord's guardrails, and never see destruction.