I think we have a bit of kneejerk literalism from our Protestant friends on this one. Immutability of God is up there with the Trinity in "orthodox" Christianity, East and West and in between.
This is from a sermon in 1855, by Rev. C. H. Spurgeon, entitled "The Immutability of God."
"But God is perpetually the same. He is not composed of any substance or material, but is spiritpure, essential, and ethereal spiritand therefore he is immutable. He remains everlastingly the same. There are no furrows on his eternal brow. No age hath palsied him; no years have marked him with the mementoes of their flight; he sees ages pass, but with him it is ever now. He is the great I AMthe Great Unchangeable... He never has been changed in his essence, not even by his incarnation; he remains everlastingly, eternally, the one unchanging God, the Father of lights, with whom there is no variableness, neither the shadow of a change."