In ordinary modern English, sincerity means to express your true feelings. The opposite, insincerity or lack of sincerity, is when we express feelings that are not true.
MW's meaning for sincerity is much deeper and not so simple. She is talking about "works of justice done in innocence" when she says we should "be such as we appear and appear such as we are" (We do acts and speak the way we really believe). "Works of juctice done in innocence" means good works done with the right attitude, with genuine, respectful and unselfish love. We talk about "having a pure intention" which means our reason for doing this is only to serve the other person well, not to get anything for myself, not even praise or thanks or a good feeling about myself. By doing in this way, we give glory to God because the Spirit of love shines through our lives.
Being "such as we appear" and appearing "such as we are" is quite near the modern meaning of sincerity but it is about more than feelings. The opposite of this sincerity is hypocrisy. Jesus hated hypocrisy, especially in religious leaders whose words and clothes and responsibilities were connected with God but their hearts were far away. Especially, their hearts were cold, not loving, and they were not open to hear the message of Jesus because it was different from their idea. So they closed their hearts and were critical and negative.
When we think of who we are and how we must appear, we are first of all the imperfect, beloved, adult children of God, each one with different gifts and weaknesses. And we are disciples and close companions of Jesus, who have recieved his Spirit and his call to work together in the Church for his kingdom. We must try to live the Christ life we say we believe is in us through baptism, the life of the Spirit we say we believe is in us through confirmation. We must hear the word of God and keep it alive in our ordinary daily life, like branches on God's vine. How will people recognise us as followers of Jesus? By our love (It's not how much we can do or how great we can achieve).
And because we have our own weaknesses as well as our own gifts, we don't pretend we are perfect. That is simply not true. Because we are not God and we don't know everything, we don't behave or talk as if we know everything. That is simply not true. Truth, which Jesus and MW both loved very much, is very closely connected to MW's idea of sincerity. We try to know the truth and to speak the truth as much as we can. But sincerity is also about living the truth of who we are and what we believe (even people don't agree with us, we have to be true to ourselves).
A modern English word for this is integrity. Like wisdom, most good people value integrity very highly, but like wisdom, we don't see much integrity in our world. It is not common but it is very precious. Like wisdom, it is a sign of being a mature person filled with the Spirit. Integrity also means wholeness. We can think about meaning of the word "integrated" where different parts have come together to make one whole thing, or "disintegrated" where something whole has broken into different parts. On our lives journey, we must learn with God's grace and human help to integrate the different parts of our personality and the different experiences of our life (good and bad) into a living whole. We can't live freely or wholly with parts of our life kept separate from each other - a sinful part, a holy part, a daughter part, a sexual part, a professional part, a wounded part, an intellectual part, etc. When some parts are hidden or rejected, we are not whole and we are not free. We can't live happily or serve with integrity. We need to bring all we are to God for healing, for blessing, for life - so that we can be good instruments of God's peace for others. (God wants us to be the best person we can be. That's why God created us).
In other places, MW uses the word "verity" in connection with this idea of sincerity. "Verity" is a very old word which is not used in ordinary modern English. Its nearest meaning is "truth" but for MW it means more than we usually mean when we say "truth". Maybe it is like when Jesus says "I am the way, I am the life, and I am the truth". Truth or verity is like godliness (God-likeness, goodness, holiness) and MW says it is not our goodness but God's goodness in us. This truth or verity is like the glory of God which can be seen even in the most ordinary situations or the most ordinary people. MW says that in our way, we are called to do ordinary things well and this is verity.
This gives glory to God!
M.C.H.