Unalterable sounds closer to what you mean, at least to me. Immutable while considered a synonym to unalterable has a more permanent ring to it, meaning even if change was required, it is impossible to happen.
According to the example in this link , there seems to be a condition for change when unalterable is being used as a word.
the constitution was unalterable without the king's consent
So your "not allowed to be changed" aspect of the question means it could be changed if needed, and unalterable seems like the best option.