**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][1]  , 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.



  [1]: https://www.lexico.com/en/definition/unalterable