We live in a world where we're told so frequently that everyone is entitled to their own opinions and their own lifestyle. We're told "to each his own" and anyone who thinks differently is labeled as close-minded and hateful. Is this okay? Is this the way God designed the world?
No, it isn't. God clearly expressed His standard that He expects us to live up to...and by "us" I mean Christians. We are supposed to be a standard that can lead the world to Christ. For more on that standard, read here.
So now, what about the rest of the world? They're supposed to follow the rules, too, right? We need to tell them when they're sinning, right? Wrong.
The Bible is very clear about the fact that we need to hold each other accountable in Matthew 18. However, notice that last line...how are you supposed to treat a pagan? Well, for one, you are supposed to love them. Read 1 Corinthians 13 and replace the word "love" with your name. If each phrase is true, then you're doing a good job of loving others. Notice, it never says to condemn. We are told in 1 Corinthians 5:12-13 to mind our own business.
If your unsaved neighbor sells drugs and dressed immodestly, your job is to love them and set a good, godly standard, and leave it at that. If your unsaved cousin is gay, you love them and set a good, godly standard, and leave it at that.
I feel I
should add that if you pick and choose which parts of the Bible you
want to follow, you need to seriously consider your salvation. When
someone has truly accepted Christ and been filled with the Holy Spirit,
they will be convicted of their wrongs and will begin to change. One who
outwardly claims to follow Christ, but inwardly continues to blatantly
choose sin is one who we should avoid. These people are liars and will
try to warp our perceptions of Truth.
In conclusion...yes, right and wrong definitely exist. Matthew 7: 13-14 says “Enter through the narrow gate. For wide is the gate and broad is the road that leads to destruction, and many enter through it. But small is the gate and narrow the road that leads to life, and only a few find it." So, we can draw from that that there are far more ways to be wrong, than ways to be right. God does not says "to each his own." Psalm 18:30 says that His way is perfect, so it's our job as Christians to study His word and follow His way.