The claim that blockchains are immutable seems to have originated sometime in 2014. Craig Wright then continued that belief in countless writings. The truth, as is usually the case with anything Craig Wright says, is very dfifferent.
Factually blockchains are not at all immutable - they are consensus driven.
Being consensus driven means that blockchains actually are mutable. In fact, not only are they mutable, the two largest projects in cryptocurrency have proven they are mutable.
To be immutable would mean that if something is recorded on the blockchain it can never be removed from the blockchain. The exact definition of immutable means unchanging over time or unable to be changed.
Being consensus driven means something very different than immutable. Being consensus driven means that blockchains are defined by what the majority of people running the blockchain say. If there is a consensus to remove data from the blockchain it can be removed and as such is not immutable.
Muting Bitcoin - The bitcoin Hack
If we look at the world first and largest blockchain, that of Bitcoin, we can easily show this to be so.
On August 15, 2010 block 74638 contained a seemingly impossible set of transactions. In fact there were transactions for three addresses containing 184,467,440,737.09551616 bitcoins. Two addresses received 92 billion bitcoin and 1 address received a fee of 0.1 bitcoin.
This was known as the value overflow incident.
Within 5 hours this bug was fixed and a softfork was performed to remove the transactions - as we all know there were never supposed to be more than 21 million bitcoin, so clearly 184 BILLION should not have existed.
The fact this soft fork was able to take place, means that the blockchain data can in fact be muted.
Now some may argue that the fact the chain had a softfork means that the data was not actually muted but rather a new chain of new data was created. This is in its most technical terms true, however the old chain of data was no longer Bitcoin, so the blockchain that is Bitcoin was muted.
This wasn't the only chain ever to have muted either.
Muting Ethereum - the DAO hack
The second most popular chain is that of Ethereum and they to have muted data.
In 2016 a DAO hack took place and ethereum decided that the hack was unacceptable so they were going to roll back those transactions. Unlike with bitcoin, there was not a full consensus so a hardfork was required.
Ethereum hardforked from the (at the time) new Ethereum Classic, which decided they didn't approve of a rollback.
Just as was the case with bitcoin, the data of the Ethereum blockchain was muted, but the original data in this case continued to exist in the ethereum classic chain. As such the ethereum blockchain was muted.
Why is any of this important to understanding blockchain?
It is important to realize a blockchain can be muted because it is important to know that a closed private blockchain cannot by default be trusted.
It was recently announced that Russia plans to hold a constitutional vote using blockchain technology. The question one needs to ask themselves is who will control that blockchain and who will be able to record the data of that blockchain.
The fact that blockchains can in fact have data altered by consensus means one cannot and should not by default trust the data, What happens if only the government of Russia controls the data, and they decide to alter it? At that point showing a blockchain saying "see this is what the people voted for" cannot be trusted.
One needs an outside audit to take place of the data, and that data would need to be verified accurate by each person that voted. This is just as bad if not worse than existing systems in that situation.
If people simply blindly trust that a blockchain cannot be altered then governemnets, banks, and corporations can use private blockchains to mislead and lie to people. The blockchain becomes no more trustworthy than any other database or ledger of data.