Not according to Him and His word. No we can never decided who is truly saved, however, we will "know them by their fruits". If they are living in open rebellion to God, then they are not truly proclaiming to be a Christian no matter what their lips say. And they are certainly not setting a good example for others to follow, proclaiming their sin to not be sin.
So, if your read the Bible, you know we're called TO judge. Matthew 7:1 makes it clear though not to be a hypocrite and prepare to be judged by your own fruit.
We cannot know the heart, God does. But we can and should gently correct one who professes Christ with his mouth, yet denies him in his actions.
Homosexuality IS, with no doubt, sin and an abomination before God. Even if you attempted to justify it, you still run into the fact that a) Only a man and woman can be married in God (despite recent secular rulings to the contrary). and b). sexual relations outside of marriage is also a sin. So there is really no loophole for homosexuality. Fortunately, it's made quite clear that it's a sin, so we don't have to resort to logic even. It's just flat out stated.
Have true Christians engaged in homosexual acts? No doubt. Have they murdered, robbed, committed adultery, taken the Lord's name in vain, etc? Of course. Christians still sin... But the difference is that in a Christian the Holy Spirit lives in us and convicts us of that sin... therefore we never do it willingly or in rebellion.