Yes.....but this does not actually change immutability. Instead it proves the attribute.
Saying it doesn't make it so.
Why is it that I can't get anyone to make an actual argument?
Maybe this will kick start things....
Socrates: "Then it must also be the case, Adeimantus, that if something is in the best possible condition, it cannot undergo any change at all, either for the better or for the worse."
Adeimantus: "Of course not."
Socrates: "For in either case, the change would be toward something less perfect, or it would be making it worse, and that cannot be true of something in its best state. So it follows that the gods, since they are perfect, do not change."
Adeimantus: "It certainly does."
That passage in Plato's Republic is THE source of the doctrine of immutability. It was Christianized by Augustine of Hippo. There are a great many passages from Augustine that I could quote but here's just a sample....
“And I was looking for the nature of the Good, which is that which is entirely immutable. And I was considering that the nature of God is good, for I saw that nothing can be better than God, and I was seeking the nature of God with the whole of my heart. For I was not so mad as to suppose that you, O Lord, could change for the worse, or could be diminished in any way. I knew that the nature of Your truth was unchangeable. And I knew that You were the same, even while I was in a state of confusion. I was in a great storm of doubt, but I was able to see that you are the foundation of all things and that in you there is no variation. The things that are perishable and can change are indeed far inferior to You, who are eternally true, immutable, and perfect. You, O Lord, are my God, and I shall not waver in my faith that You are unchangeable. - Confessions, Book VII, Chapter 10
“For it was clear and certain to me that what is subject to change must be inferior to that which cannot change; and so I knew that You must be unchangeable, since if any mind could conceive something better than You, the creature would surpass the Creator. ... I then perceived that the things which are perishable have their being through Him who is unchangeable; and that in Him there is no 'was' or 'will be,' but only 'is,' because He is eternal. You, O Lord, have made clear to me with great certitude that what is always true is absolutely unchangeable. For it is now as certain to me that You are, as it is certain that there is a difference between numbers being even and odd.” - Confessions, Book VII, Chapter 15
Martin Luther who kicked off the Reformation was an Augustinian monk and while he separated himself from Roman heresies that had crept their way into the church, he very much did not separate himself from the Greek heresies that had done the same. Calvin then canonized the reformation doctrines when he wrote "Institutes" and formed what we call "Calvinism", which is just a reformed version of Augustinian doctrine.
Biblically, however, we see prophesies that did not come to pass, we see God repenting of disasters that He said He would perform, we see Him changing His mind and either not destroying Israel or not blessing them to the extent that He had promised, we see things happen that God Himself says that never entered His mind, we see God watching "to see" what would happen, we see God taking steps to prevent potential problems, etc, etc, etc.