Faith and works is a false dichotomy because neither are the means to anything but experience, and what is atoning is the experience of God, and God, being the good, goodness, is found in participation with it; and this, by hearing and doing (James 1:19-27), and indeed, Matthew 7:15-21 only affirms the idea that those who do good are “in me and I in them”. Atonement has nothing to do with professions of faith, or right beliefs, or any beliefs about God at all.
How many scores of passages are there about what Jesus says about salvation? All of them are about repenting, not judging actions including our own, but instead, looking past them into a way of being in the world that is rooted much more deeply in humanity, and discovering it through love? For the literally hundreds of them in the New Testament and Old Testament, they are summed up in James, 1:27 in particular.
Put it this way:
To be a diver is not to jump any particular way into the air and fall into a pool of water. It is to understand through the experience of diving the entire nature of diving, which is far more than creatively dropping through space. However, it is impossible to become a diver without doing just that; diving. Diving must be an experience, and so too must atonement.
Salvation indeed requires works because one can only experience salvation through the sacramental act of goodness; salvation is not the act but the experience of the meaning of goodness through participation with it, by the doing of it, participation naturally requiring action. Faith is not belief but the draw to the good, the desire to do it in the first place. Grace and faith, having nothing to do with anything but God, are his gifts to humanity. Our part is responding to the draw, in it.