Quakers recommend that, in our relations with each other, we should strive to respond to "that of God within everyone." In my own thinking, I have always related this to a supreme principle of respect. At least part of respect includes believing that everyone is capable of goodness. And at least part of the recommendation to look for and respond to "that of God" within everyone is also to assume that everyone is capable of goodness.
Immanuel Kant proposes something similar in his moral theory. One formulation of his "categorical imperative" is "Act in such a way that you treat humanity, whether in your own person or in the person of another, always at the same time as an end and never simply as a means" (Grounding for the Metaphysics of Morals, 429, trans. James W. Ellington, Hackett Publishing Company,  1981).
For Kant, understanding people as "ends" is the same as understanding them as "rational agents." By this, he means that people set their own goals, and thus are sources of new activity in the world. Kant then connects human rationality to the concept of "goodness" in the following way. Ultimately, the "true function" of our rational nature "must be to produce a will which is not merely good as a means to some further end, but is good in itself" (396). He makes this comment on the heels of just having argued that rationality is not for the purpose of survival alone--instinct can and does aid in the survival of many other living organisms. Nor is the purpose of rationality to ensure happiness--it doesn't do a very good job at that! We cannot really plan for our own happiness (even if we do all desire it). So there is some other purpose for our having rationality: producing a will that is good in itself (that wills good for the sake of goodness alone).
When our will is thus purified, the goals that we set and the activity that results from our trying to fulfill these goals brings new goodness into the world. By treating people "as ends," we respect them as potential sources of new goodness for the world. And by "responding to that of God within everyone," we try, in our relations with others, to encourage them to bring that potential goodness forth.
The early Quakers believed that humans can reach a kind of perfection in life, and they too connected this notion with a kind of purification of will (see for example Barclay's Proposition VIII, in his Apology [1675/1678]). Barclay believed that it is an insult to God to think that God created us so badly that a kind of human perfection is impossible. He also worries that a doctrine that human perfectibility is impossible can make us all too willing to accept our shortcomings.
"What is the purpose of such a strange doctrine? The imperfection of Christians comes either from God or from themselves. If it is of their own doing, it must be because they fall short of using the power of obedience that was given them. In that case, they were capable of achieving God's will with his aid. But our opponents deny this, so they are not to be blamed for continuing in sin since they are incapable of doing otherwise" (Barclay's Apology in Modern English, edited by Dean Freiday, p. 158).
Barclay does not believe that reaching a kind of perfection makes us invulnerable to future sin or error. "If [those who have attained a measure of perfection] are not watchful they may fall into iniquity and lose it. Many good and holy men have had their ups and downs of this kind" but sin "does not destroy him altogether or make it impossible to rise again" (156). He goes on to argue that, "nevertheless a state can be attained in this life in which it becomes so natural to act righteously that a condition of stability is achieved in which sin is impossible" (157).
Do Quakers today still believe that this kind of perfectibility is possible?