In the introduction to the Olney Hymns:
The views I have received of the doctrines of grace [Calvinism] are essential to my peace; I could not live comfortably a day, or an hour, without them. I likewise believe . . . them to be friendly to holiness, and to have a direct influence in producing and maintaining a gospel conversation; and therefore I must not be ashamed of them. (Works, 3:303)
Works, Vol. 6, p. 199
Though a man does not accord with my views of election, yet if he gives me good evidence that he is effectually called of God, he is my brother; though he seems afraid of the doctrine of final perseverance; yet, if grace enables him to persevere, he is my brother still. If he loves Jesus, I will love him, whatever hard name he may be called by, and whatever incidental mistakes I may think he holds. His differing from me will not always prove him to be wrong, except I am infallible myself.
Works, Letter IX, "On the Doctrines of Election and Final Perseverance"
https://www.gracegems.org/Newton/09.htm
How can we account for the conversion of a soul to God, unless we likewise admit an election of grace? The work must begin somewhere. Either the sinner first seeks the Lord, or the Lord first seeks the sinner. The former is impossible, if by nature we are dead in trespasses and sins; if the god of this world has blinded our eyes, and maintains the possession of our hearts; and if our carnal minds, so far from being disposed to seek God, are enmity against him.
We maintain, that no doctrines or means can change the heart, or produce a gracious conversation, without the efficacious power of Almighty grace.
Memoirs of the Life of the Late Rev. William Grimshaw, With Occasional Reflections by John Newton, 1799
They who avow the doctrines distinguished by the name of Calvinistic, ought, if consistent with their own principles, to be most gentle and forbearing of all men, in meekness instructing them that oppose. With us, it is a fundamental maxim, that a man can receive nothing but what is given him from heaven (John 3:27). If, therefore, it has pleased God to give us the knowledge of some truths, which are hidden from others, who have the same outward means of information; it is a just reason for thankfulness to Him, but will not justify our being angry with them; for we are no better or wiser than they in ourselves, and might have opposed the truths which we now prize, with the same eagerness and obstinacy, if His grace had not made us to differ. If the man, mentioned in John 9, who was born blind, on whom our Lord graciously bestowed the blessing of sight, had taken a cudgel and beat all the blind men he met, because they would not see, his conduct would have greatly resembled that of an angry Calvinist.
On Controversy
Of all people who engage in controversy, we, who are called Calvinists, are most expressly bound by our own principles to the exercise of gentleness and moderation.
If, indeed, they who differ from us have a power of changing themselves, if they can open their own eyes, and soften their own hearts, then we might with less inconsistency be offended at their obstinacy: but if we believe the very contrary to this, our part is, not to strive, but in meekness to instruct those who oppose.
“If peradventure God will give them repentance to the acknowledgment of the truth.” (2 Timothy 2:25)
If you write with a desire of being an instrument of correcting mistakes, you will of course be cautious of laying stumbling blocks in the way of the blind or of using any expressions that may exasperate their passions, confirm them in their principles, and thereby make their conviction, humanly speaking, more impracticable.
I am afraid there are Calvinists, who, while they account it a proof of their humility that they are willing in words to debase the creature, and to give all the glory of salvation to the Lord, yet know not what manner of spirit they are of. Whatever it be that makes us trust in ourselves that we are comparatively wise or good, so as to treat those with contempt who do not subscribe to our doctrines, or follow our party, is a proof and fruit of a self-righteous spirit. Self-righteousness can feed upon doctrines, as well as upon good works; and a man may have the heart of a Pharisee, while his head is stored with orthodox notions of the unworthiness of the creature and the riches of free grace.