For I am the LORD, I change not... - Malachi 3:6a
Jesus Christ the same yesterday, and to day, and for ever.
Be not carried about with divers and strange doctrines. For it is a good thing that the heart be established with grace; not with meats, which have not profited them that have been occupied therein.
- Hebrews 13:8-9
There's also another good reason God doesn't change...
That we henceforth be no more children, tossed to and fro, and carried about with every wind of doctrine, by the sleight of men, and cunning craftiness, whereby they lie in wait to deceive;
But speaking the truth in love, may grow up into him in all things, which is the head, even Christ:
From whom the whole body fitly joined together and compacted by that which every joint supplieth, according to the effectual working in the measure of every part, maketh increase of the body unto the edifying of itself in love.
- Ephesians 4:14-16