Psa 55:19 God will give ear and humble them, he who is enthroned from of old, Selah because they do not change and do not fear God.

The NIV renders Psalms 55:19 as:

God, who is enthroned from of old, who does not change— he will hear them and humble them, because they have no fear of God

The NIV points the prepositional phrase “who does not change” at God while all other major versions (KJV, NKJV, ESV, NET) point the phrase at man. In context of man, the phrase would be referring to man’s stubbornness. God is judging man because man is stubborn.

In Thomas Cook’s commentary, he tellingly describes the purpose of rendering the phrase as applying to God:

Some render it: They are not changed, and they fear no God. And Mudge reads the whole verse, God shall hear, and he that abideth of old, with whom are no changes, shall humble them, since they fear not God: as much as to say, “That immutable Being (with a glance at the infidelity of men) who was always faithful to his promises and friends, would support him, and humble them.”

The telling aspect is how arbitrary the same phrase can both be applied to man and God. When used of God, it is taken as a metaphysical claim of immutability in the very same context which would be used of steadfastness if applied to man.

The context of Psalms 55 is a call of King David for justice. He calls on God to act and to save him. Like many of these Psalms, the chapter then leads into a proposed punishment of the wicked. Because the wicked have attacked David for so long, without changing, they will be punished.
The verse is not about complete metaphysical immutability of man (nor God). It is using normal language to describe man’s unwillingness to repent. Similar language is used about men who remain faithful in Psalms 15:4. The “not changing” is limited to a character statement, and not to be understood outside that scope.