Is it a sin to wonder if someone who claims to be a Christian really is? I have an uncle who claims to be a Christian but I just don't see the fruits of this in his life. In fact in many ways I see a lot of non-Christian attitudes and behavior in his life. I often wonder about the state of his "salvation". I hope that I am wrong but I can't help but have my doubts. I do pray for him but that is really all I can do.
I don't find anything that says it is a sin to wonder about another's sincerity. How you act as a result may be wrong if you let your thoughts cause you to do harm to the reputation or physical well-being of another.
"You shall know them [false prophets] by their fruits." (Matthew 7:16) I have heard some people say, based on this passage, "we are not called upon to be judges, but we are allowed to be fruit inspectors." I'm not sure that is what Jesus had in mind when he said this, but he did mean that those who teach or profess one thing and practice something else give themselves away as not being followers of the word of God.
If someone shows by their life that they are not "walking in the light" (1 John 1:7), then all we can do is pray. First, pray that they may "bring forth fruit fitting to repentance." (Matthew 3:8) Second, we should pray that their actions do not cause others to ignore their own salvation. That is, the danger of one living in their old ways is that others will see them and say, "If that's how a Christian lives, then I might as well stay the way I am."