We should have a single intention, namely to do God's will. Sincerity is about carrying out our intention. Sincerity means that we actually do what we aim at by simplicity. We walk continually on in the highway of holiness, in the paths of justice, mercy, and truth. If you think about it all people are sincere about some things.
Sports fans are very sincere about their particular team.
Some people are very sincere about their political party. Others are equally sincere about family or money. But Paul wants to emphasize that he is not talking about that kind of sincerity. He is talking about a heartfelt earnestness that focuses on God. His point is that what ever does not have God as its object and end is ultimately unimportant.